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Full text of "Hurricane climatology for the Atlantic and Gulf coasts of the United States"

DOC. 

C 55.13: 
NWS38 



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NOAA Technical Report NWS 38 

Hurricane Climatology 
for the Atlantic and 
Gulf Coasts of the 
United States 



Silver Spring, MD 
April 1987 



The 



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Study completed under agreement EMW-84-E-1589 for 
FEDERAL EMERGENCY MANAGEMENT AGENCY 



U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Weather Service 



NOAA TECHNICAL REPORTS 
National Weather Service Series 

The National Weather Service (NWS) observes and measures atmospheric phenomena; develops and distrib- 
utes forecasts of weather conditions and warnings of adverse weather; collects and disseminates weather 
information to meet the needs of the public and specialized users. The NWS develops the national 
meteorological service system and improves procedures, techniques, and dissemination for weather and 
hydrologic measurements, and forecasts. 

NWS series of NOAA Technical Reports is a continuation of the former series, ESSA Technical Report 
Weather Bureau (WB). 

Reports listed below are available from the National Technical Information Service, U.S. Depart- 
ment of Commerce, Sills Bldg. , 5285 Port Royal Road, Springfield, VA 22161. Prices vary. Order by 
accession number (given in parentheses). 

ESSA Technical Reports 

WB 1 Monthly Mean 100-, 50-, 30-, and 10-Millibar Charts January 1964 through December 1965 of the 
IQSY Period. Staff, Upper Air Branch, National Meteorological Center, February 1967, 7 p, 
96 charts. (AD 651 101) 

WB 2 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1964 (based on observations of the 
Meteorological Rocket Network during the IQSY). Staff, Upper Air Branch, National Meteorologi- 
cal Center, April 1967, 16 p, 160 charts. (AD 652 696) 

WB 3 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1965 (based on observations of the 
Meteorological Rocket Network during the IQSY). Staff, Upper Air Branch, National Meteorologi- 
cal Center, August 1967, 173 p. (AD 662 053) 

WB '+ The March-May 1965 Floods in the Upper Mississippi, Missouri, and Red River of the North Basins. 
J. L. H. Paulhus and E. R. Nelson, Office of Hydrology, August 1967, 100 p. 

WB 5 Climato logical Probabilities of Precipitation for the Conterminous United States. Donald L. 
Jorgensen, Techniques Development Laboratory, December 1967, 60 p. 

WB 6 Climatology of Atlantic Tropical Storms and Hurricanes. M. A. Alaka , Techniques Development 
Laboratory, May 1968, 18 p. 

WB 7 Frequency and Areal Distributions of Tropical Storm Rainfall in the United States Coastal Region 
on the Gulf of Mexico. Hugo V. Goodyear, Office of Hydrology, July 1968, 33 p. 

WB 8 Critical Fire Weather Patterns in the Conterminous United States. Mark J. Schroeder, Weather 
Bureau, January 1969, 31 p. 

WB 9 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Mb Surfaces for 1966 (based on meteorological rocket- 
sonde and high-level rawinsonde observations). Staff, Upper Air Branch, National Meteorological 
Center, January 1969, 169 p. 

WB 10 Hemispheric Tele connect ions of Mean Circulation Anomalies at 700 Millibars. James F. O'Connor, 
National Meteorological Center, February 1969, 103 p. 

WB 11 Monthly Mean 100- , 50-, 30-, and 10-Millibar Charts and Standard Deviation Maps, 1966-1967. 
Staff, Upper Air Branch, National Meteorological Center, April 1969, 124 p. 

WB 12 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1967. Staff, Upper Air Branch, 
National Meteorological Center, January 1970, 169 p. 

NOAA Technical Reports 

NWS 13 The March-April 1969 Snowmelt Floods in the Red River of the North, Upper Mississippi, and Mis- 
souri Basins. Joseph L. H. Paulhus, Office of Hydrology, October 1970, 92 p. (COM-71-50269) 

NWS 14 Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1968. Staff, Upper Air Branch, 
National Meteorological Center, May 1971, 169 p. (COM-71-50383) 

NWS 15 Some Climato logical Characteristics of Hurricanes and Tropical Storms, Gulf and East Coasts of 
the United States. Francis P. Ho, Richard W. Schwerdt, and Hugo V. Goodyear, May 1975, 87 p. 
(C0M-7 5-1 1088) 

(Continued on inside back cover) 



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NOAA Technical Report NWS 38 

Hurricane Climatology 
for the Atlantic and 
Gulf Coasts of the 
United States 

Francis P. Ho, James C. Su, Karen L. Hanevich, 
Rebecca J. Smith and Frank P. Richards 
Silver Spring, MD 

April 1987 



Government Document 
Book Stacks 



Study completed under agreement EMW-84-E-1589 for 
FEDERAL EMERGENCY MANAGEMENT AGENCY 



U.S. DEPARTMENT OF COMMERCE 

Malcolm Baldrige, Secretary 

National Oceanic and Atmospheric Administration 

Anthony J. Calio. Under Secretary 

National Weather Service 

Richard E. Hallgren, Acting Assistant Administrator 



Digitized by the Internet Archive 

in 2012 with funding from 

University of Illinois Urbana-Champaign 



http://archive.org/details/hurricaneclimatoOOhofr 






TABLE OF CONTENTS 

Page 



Abs tract 1 

1 . Introduction I 

1 .1 Authorization. 1 

1.2 Purpose 2 

1.3 Scope of report 2 

1.4 Relation to flood insurance studies 4 

1.5 Previous studies. 5 

2. Data 5 

2.1 Introduction 5 

2.2 Sources of data 6 

2.3 Hurricane central pressure (P Q ) data 23 

2.3.1 Central pressure criteria based on balanced wind model 2 4 

2.3.2 Central pressure adjustments 2 4 

2.3.3 Revised central pressure from previous studies 2 5 

2.4 Hurricane radius of maximum winds (R) data 2 5 

2.4.1 Source of radius of maximum winds 2 6 

2.4.1.1 Radius of maximum winds from aerial reconnaissance 26 

2.4.1.2 Radius of maximum winds from wind records 2 7 

2.4.1.3 Radius of maximum winds from eye radius. 28 

2.4.1.4 Radius of maximum winds from pressure fit...... 2 8 

2.4.1.5 Radius of maximum winds from Monthly Weather Review 28 

2.5 Speed and (T) direction (9) of forward motion 2 8 

2.5.1 Source of T and 9 data 28 

2.5.2 T and 9 data used in probability distributions 30 

3. Meteorological parameters and their interrelations......... 30 

3.1 Introduction. 30 

3.1.1 Overview of the statistical study... 30 

3.1.2 Scope of the chapter 3 1 

3.2 Considerations of data samples for statistical tests 31 

3.2.1 Forward speed 32 

3.2.2 Forward direction 34 

3.3 Homogeneity of the hurricane data samples.. 3 4 

3.3.1 Methods for testing the homogeneity of storm parameters 3 5 

3.3.2 Comparison of results from different homogeneity tests 3 7 

3.3.2.1 Meteorological method 37 

3.3.2.2 Cluster analysis 38 

3.3.2.3 Discriminant analysis 38 

3.3.2.4 Principal component analysis 39 

3.3.3 Selection of hurricane groups for independence testing 40 

3.3.3.1 Gulf coast 42 

3.3.3.2 Florida coast 42 

3.3.3.3 Atlantic coast 43 



Page 

3.4 Interrelations between hurricane parameters 43 

3.4.1 Brief review of previous studies 43 

3.4.2 Methods for testing the interrelations between hurricane 

parameters 44 

3.4.2.1 Contingency table with Chi-square test 44 

3.4.2.2 Spearman test 44 

3.4.3 Comparison of results from different independence tests 45 

3 .5 Discussion 45 

4. The joint probability question: Central pressure versus 

radius of maximum winds 50 

4 .1 Introduction 50 

4.2 Central pressure versus radius of maximum winds 50 

4.3 Meteorological analysis 52 

4.4 Discussion of analysis 55 

4 .5 Conclusions 59 

5. Other joint probability questions 59 

5 . 1 Introduction 59 

5.2 Forward speed versus direction of storm motion 60 

5.3 Central pressure versus direction of storm motion 61 

5.3.1 Gulf coast 61 

5.3.2 Atlantic coast.. 64 

5.3.2.1 Atlantic coast, south of 33 ,5°N 64 

5.3.2.2 North Atlantic coast 66 

5.4 Cape Hatteras area 66 

5.4.1 Parameters for landfalling hurricanes from northeast 

quadrant.. 66 

5.4.2 Parameters for landfalling hurricanes from southeast 

quadrant 67 

5.4.3 Landfalling track frequency 67 

6. Frequency of hurricane and tropical storm occurrences 67 

6.1 Classification of hurricanes and data 67 

6.2 Frequency of landfalling tropical cyclones..... 72 

6.2.1 Direct-count method........ 72 

6.2.1.1 Objective smoothing procedure 75 

6.2.1.2 Evaluation of procedure 7 5 

6.2.2 Discussion of results 7: 

6.2.2.1 Areas of high entry frequencies 7 

6.2.2.1 (a) Northwest Florida 77 

6.2.2.1 (b) South Florida 77 

6.2.2.1 (c) Upper Texas coast 78 

6.2.2.1 (d) Cape Hatteras 78 

6.2.2.2 Areas of low entry frequencies 78 

6.2.2.2 (a) East coast 78 

6.2.2.2 (b) Gulf coast 78 

6.3 Frequency of exiting tropical cyclones 78 

6. 3.1 Analysis * 78 

6.3.2 Results and discussion 

6.3.2.1 Gulf coast 79 



iv 



Page 

6.3.2.2 Atlantic coast 79 

6.3.2.3 Application in tide-frequency analysis 79 

6.4 Frequency of alongshore tropical cyclones 81 

6.4.1 Analysis 81 

6.4.2 Results and discussion 85 

7. Central pressure 85 

7 .1 Introduction 85 

7 .2 Analysis 86 

7.3 Results 89 

7.3.1 Pressure minima 89 

7.3.1.1 South Florida minimum..... 89 

7.3.1.2 South Texas minimum 92 

7.3.1.3 Carolinas and southern New England minima 92 

7.3.1.4 Mississippi Delta minimum 92 

7.3.2 Pressure maxima 92 

7.3.2.1 Cross City, Florida, maximum 92 

7.3.2.2 Delaware Bay maximum 93 

7.3.2.3 Jacksonville maximum.... 93 

7.3.2.4 Northern New England coastal maximum 93 

8. Radius of maximum winds 94 

8.1 Analysis 94 

8.1.1 Gulf of Mexico 95 

8.1.2 Atlantic coast 95 

8.2 Evaluation of the analysis 95 

8.2.1 Gulf coast 95 

8.2.1.1 Florida and Mexico minima 95 

8.2.1.2 Mississippi-Florida panhandle maximum..... 95 

8.2.2 Atlantic coast 95 

8.3 Radius of maximum winds for intense hurricanes 98 

9. Speed and direction of storm motion 98 

9.1 Speed of storm motion 98 

9.1.1 Forward speed of landf ailing tropical cyclones 98 

9.1.1.1 Analysis 98 

9.1.1.2 Results and discussion 98 

9.1.2 Forward speed of bypassing tropical cyclones 102 

9.2 Direction of storm motion 102 

9.2.1 Direction of storm motion for landfalling tropical 

eye lones 102 

9.2 .1.1 Analysis 102 

9.2.1.2 Results and discussion 103 

9.2.1.2 (a) Gulf coast 106 

9.2.1.2 (b) East coast, south of Cape Hatteras 107 

9.2.1.2 (c) East coast, north of Cape Hatteras 107 

9.2.1.3 Areas of discontinuous direction profile 107 

9.2.2 Direction of storm motion for bypassing tropical cyclones... 107 

10. Adjustment of hurricane intensity for filling overland 108 

10.1 Introduction 108 

10.2 Index for overland filling 108 



Page 



10.3 Previous observational studies .. 109 

10.4 Analysis of data 109 

10.5 Filling rates by region 110 

10.6 Results 121 

11. Application of hurricane parameters 123 

11.1 Introduction 123 

11.2 Landfall point 123 

11.3 Peripheral pressure 124 

11.4 Probability distributions of hurricane parameters and 

frequency of occurrence 12 4 

11.5 Applications of profiles of probability distributions for 

hurricane parameters. 12 7 

11.6 Exiting tropical cyclones 13 6 

12. Summary and discussion... 136 

12.1 Frequency of tropical cyclone occurrences 13 7 

12.2 Probability distribution of storm parameters 138 

12.3 Independence of parameters.... 138 

Acknowledgments 139 

References 140 

Appendix A Detailed analysis of selected storms 147 

A.l Introduction 147 

A.2 Hurricane Alicia, August 15-21, 1983 147 

A .2 .1 Introduction. 147 

A.2 .2 Previous reports 147 

A.2 .3 Sources of data 148 

A.2 .4 General meteorological situation 149 

A.2 .5 Detailed meteorological analysis... 149 

A.2. 5.1 Storm track 149 

A.2 .5.2 Forward speed... 150 

A.2 .5.3 Central pressure 152 

A.2. 5. 4 Wind analysis 154 

A.2. 5. 5 Radius of maximum winds 156 

A.2 .6 Discussion 159 

A.3 Hurricane David, September 2-5, 1979 160 

A. 3 .1 Introduction 160 

A.3 .2 Previous studies * 162 

A.3 .3 Aircraft data..... 163 

A.3. 4 Central pressure 164 

A.3 .4.1 P from aerial reconnaissance. 164 

A.3 .4.2 P from land station observations 164 

A. 3. 4.3 Pressure fit at the coast 164 

A.3. 4. 4 Time variation of P 164 

A.3 .5 Radius of maximum winds 170 

A.3. 5.1 R from aerial reconnaissance...... 170 

A. 3. 5.2 R from land station observations 170 

A.3 .5.3 Time variation of radius of R 174 

A. 4 Hurricane Allen, August 2-10, 1980 174 

A. 4.1 Introduction . 174 

A. 4.2 Previous reports 176 

A. 4. 3 Reconnaissance flight data.. 177 



Page 

A. 4. 4 Central pressure analvsis 177 

A. 4. 5 Wind analvsis 177 

A. 4. 6 Time variation of central pressure and radius of maximum 

winds ' 1 82 

A. 4. 7 Relation of P Q and R in Hurricane Allen 182 

Appendix B Statistical methods for tests of homogeneitv and 

independence 185 

B .1 Introduction 18 5 

B .2 Methods for the test of homogeneity 185 

B.2.1 Cluster analysis 185 

B.2.1.1 Description of the method 185 

B.2.1. 2 Rationale for choice 186 

B.2.1. 3 Limitations of the method 187 

B.2.1. 4 Interpretation of the results 187 

B.2.2 Discriminant analysis 187 

B.2.2.1 Description of the method 187 

B.2.2 .2 Rationale for choice 187 

B.2.2 .3 Limitations of the method 187 

B.2.2. 4 Interpretation of the results 188 

B.2.3 Principal component analysis 188 

3.2.3.1 Description of the method 188 

B.2.3 .2 Rationale for choice 188 

B.2.3 .3 Limitations of the method 188 

B.2.3 .4 Interpretation of the results 188 

B.2.4 Mann-Whitney test 189 

B.2.4.1 Description of the method 189 

B.2.4.2 Rationale for choice 190 

B.2.4.3 Limitations of the method 190 

B.2.4.4 Interpretation of the results 190 

B.3 Methods for the test of independence 190 

B.3.1 Spearman test 191 

B.3. 1.1 Description of the method..... 191 

B.3. 1.2 Rationale for choice. 191 

B.3. 1.3 Limitations of the method 191 

B.3. 1.4 Interpretation of the results 191 

B.3. 2 Contingency table with Chi-square test 192 

B.3 .2.1 Description of the method 192 

B.3 .2 .2 Rationale for choice 192 

B.3. 2.3 Limitations of the method 192 

B.3 .2 .4 Interpretation of the results 192 

Appendix C Plotting position formula 192 

C .1 Introduction 192 

C.2 Criteria for evaluation 192 

C.3 Evaluation of plotting position formulae 194 

C.4 Comparison of formulae 194 



LIST OF FIGURES 

Number Page 

1 Locator map with coastal distance intervals marked (nmi) 3 

2 Hourly observations of wind speed and direction, and distance of 

Allen's center from Brownsville, Texas 27 

3 Radius of maximum winds versus inner radar eye radius 2 9 

4 Difference between the radius of maximum winds and the inner radar 

eye radius versus maximum wind speed 2 9 

5 Forward speed of landfalling hurricanes and tropical storms versus 

milepost (a) along the Gulf coast of Florida, and (b) along the 
Atlantic coast 33 

6 Possible homogeneous regions for landfalling hurricane 

parameters * 36 

7 Plot of the second principal component versus the first principal 

component 40 

8 Central pressure of landfalling hurricanes versus milepost 41 

9 Interrelations between parameters of landfalling hurricanes for 

the Gulf and Atlantic coasts of the United States 46 

10 Landfalling hurricane parameters versus milepost for the Atlantic 

coast. 48 

11 Location and minimum central pressure of extreme hurricanes 54 

12 Tracks of extreme hurricanes 56 

13 Same as Figure 12 57 

14 Plot of P versus R for extreme hurricanes listed in Table 16 58 

15 Scatter diagram of direction versus speed of forward motion for 

hurricanes landfalling on the Atlantic coast 60 

16 Probability distribution of forward speed of (a) landfalling, and 

(b) alongshore hurricanes in the vicinity of Charleston, South 
Carolina, for the period 1886-1973 62 

17 Plot of forward direction versus milepost for the landfalling 

hurricanes on the Gulf coast of the United States 63 

18 Variation with latitude of direction of forward motion for 

hurricanes landfalling on the Atlantic coast... 63 



vi i i 



Number Page 

19 Histogram for direction of storm motion for the 2.5° latitude and 

longitude block centered about Key West, Florida 65 

20 Track, of tropical storms and hurricanes showing motion from 

northeast 68 

2 1 Cumulative probability curve of central pressure for landf ailing 

tropical cyclones near Wright Monument, North Carolina 69 

22 Cumulative probability curve of speed of storm motion adapted for 

landfalling tropical cyclones near Wright Monument, North 

Carolina. 69 

23 Frequency of landfalling hurricanes and tropical storms 70 

24 Smoothed coastline obtained by applying the objective smoothing 

function 71 

2 5 Map showing extensions of west coast of Florida and the Atlantic 

coast through the Florida Keys..... 73 

2 6 Count of landfalling tropical storms and hurricanes (1871-1984) 

by 50-nmi segments of a smoothed coastline 74 

27 Frequency of landfalling tropical cyclones (1871-1984) for the 

Gulf and Atlantic coasts of the United States.. 76 

28 Frequency of exiting hurricanes and tropical storms (1871-1974).... 80 

2 9 Tide frequencies at Wright Monument, North Carolina, for several 

classes of storms 81 

3 Accumulative count of hurricane and tropical storm tracks passing 

the coast at sea (1871-1984) 82 

3 1 Cumulative frequency of tropical cyclones bypassing the Gulf coast 

at selected distances offshore (1871-1984) 83 

32 Cumulative frequency of tropical cyclones bypassing the Atlantic 

coast at selected distances offshore (1871-1984) 84 

33 Cumulative probability curve of central pressure of hurricanes 

landfalling within (a) 250 nmi of milepost 250, near Corpus 

Christi, Texas, and (b) 200 nmi of milepost 1600 near Vero 

Beach Florida a 88 

3 4 Probability distribution of central pressure for hurricanes 

landfalling on the Gulf coast (1900-84) 90 

35 Same as Figure 34, but for Atlantic coast hurricanes... 91 



Number Page 

36 Cumulative probability curve of radius of maximum winds for 

hurricanes landf ailing within (a) 2 50 nmi of milepost 2 50, near 

Corpus Christi, Texas, and (b) 200 nmi of milepost 1600, near 

Vero Beach, Florida 94 

37 Probability distribution of radius of maximum winds for hurricanes 

landf ailing on the Gulf coast (1900-84) 96 

38 Same as Figure 37, but for Atlantic coast hurricanes 97 

3 9 Cumulative probability curve of forward speed of tropical cyclones 
landfalling within (a) 250 nmi of milepost 250, near Corpus 
Christi, Texas, and (b) 200 nmi of milepost 1600, near Vero 

Beach, Florida 99 

40 Probability distribution of forward speed for tropical cyclones 

landfalling on the Gulf coast (1900-84) 100 

41 Same as Figure 40, but for Atlantic coast tropical cyclones........ 101 

42 Cumulative probability curve of direction of storm motion of 

tropical cyclones landfalling within (a) 100 nmi of milepost 2 50, 

near Corpus Christi, Texas, and (b) 100 nmi of milepost 1600, 

near Vero Beach, Florida 103 

43 Probability distribution for direction of storm motion for 

tropical cyclones landfalling on the Gulf coast (1900-84) 104 

44 Same as Figure 43, but for the Atlantic coast south of Cape 

Hatteras 105 

45 Same as Figure 43 , but for the Atlantic coast north of Cape 

Hatteras 106 

46 Pressure profiles after landfall for (a) hurricane Frederick 

September 1979 and (b) Hurricane Alicia, August 1983 HI 

47 Map showing geographical regions used to study filling rates 112 

48a Variation with time after landfall of filling rate of hurricanes 

listed in region A of Table 19 114 

48b Same as Figure 48a 115 

49 Filling rates for hurricanes of various intensities for region A 

(Gulf coast, west of Apalachicola, Florida) 116 

50 Comparison of filling rates for various hurricanes crossing the 

Florida peninsula and Che filling curve for region B from 

Schwerdt et al. (1979) 118 



Number Page 

51 Filling rates for hurricanes of various intensities for region B 

(southern Florida) 119 

52 Variation with time after landfall of filling rates for Hurricanes 

Hazel (1954), Gracie (1959), and David (1979) 120 

53 Variation with time of filling rates for New England hurricanes.... 12 1 

54 Filling rate for hurricanes in region C (Atlantic coast, north of 

Georgia ) 12 2 

55 Plot of cumulative counts of alongshore storms versus distance 

from coast for Vero Beach, Florida (milepost 1600) 12 6 

56 Cumulative probability curves of P Q for designated locations....... 133 

57 Cumulative probability curve for pressure deficit at Vero Beach, 

Florida 13 5 

A.l Hurricane track for Alicia, 0000 CST August 16 through 1200 CST 

August 18, 1983 150 

A.2 Hurricane eye position obtained from radar, aircraft 

reconnaissance penetration fixes, and satellite observations 151 

A. 3 Minimum pressure recorded at land stations and by aircraft 

reconnaissance during Hurricane Alicia 152 

A. 4 Variation of minimum central pressure estimates for Hurricane 

Alicia 153 

A. 5 Hourly observations of sea-level pressure and surface wind speed 

recorded at Houston Intercontinental Airport, Texas 155 

A. 6 Same as Figure A. 5, but for Baytown, Texas 156 

A. 7 Composite isotach analysis for Hurricane Alicia, centered at 

2240 GMT, August 17, 1983 157 

A. 8 Streamline and 10-m isotach analysis for Hurricane Alicia, 

0730 GMT, August 18, 1983.. 158 

A. 9 Flight-level winds recorded along radials through the center of 

Hurricane Alicia, 1352-1433 GMT, August 17, 1983 159 

A. 10 Radius of primary and secondary wind maxima in Hurricane Alicia, 

August 17-18, 1983 160 

A.ll Track with central pressures for Hurricane David, 

September 2-5, 1979. 161 



xi 



Number Page 

A. 12 Reconnaissance flight pattern, designated as star pattern used in 

Hurricanes David and Allen 163 

A. 13 Sea-level pressure observed during passage of Hurricane David, 
(September 1979) at (a) Shuttle Airport, Florida, 
and (b) Savannah (Municipal Airport), Georgia 165 

A. 14 Pressure-profile curve during Hurricane David (a) for Florida coast 
at 2100 GMT, September 3, 1979, (b) Georgia coast at 1800 GMT, 
September 4, 1979 166 

A. 15 Central pressure (sea-level) for Hurricane David, 

September 3-5, 1979 167 

A. 16 Flight-level winds recorded along radials through the center of 
Hurricane David, (a) 2308-2356 GMT, September 2, (b) 0644- 
0748 GMT, September 4, and (c) 1751-1841 GMT, September 4, 1979.. 169 

A. 17a Wind speed and direction at Shuttle Airport, Florida, during 

the passage of Hurricane David, September 2-4, 1979.. 171 

A. 17b Wind speed and direction at Savannah, Georgia, during the passage 

of Hurricane David, September 3-5 , 1979 172 

A. 18 Radial distances (from eye center) of wind maxima in Hurricane 

David, September 2-5, 1979 173 

A. 19 Track of Hurricane Allen, August 2-11, 1980 175 

A.20 Reconnaissance flight patterns used in Hurricane Allen... 179 

A.2 1 Central pressure for Hurricane Allen, (a) August 3-7, and (b) 

August 7-10, 1980 180 

A.22 Flight-level winds recorded along radials through the center 

of Hurricane Allen, 1535-1627 GMT, August 5, 1980 181 

A.23 Flight-level winds recorded along radials through the center of 

Hurricane Allen, 1844-1945 GMT, August 7, 1980 181 

A. 2 4 Composite map of flight-level winds recorded between 02 00 and 

0400 GMT, August 9, 1980 ' 182 

A.2 5 Central pressure and radial distances (from eye center) 

of wind maxima in Hurricane Allen, August 3-10, 1980 183 

A.2 6 Concurrent observations of central pressure and radius of maximum 

winds for Hurricane Allen, August 3-9, 1980 184 

B.l Levels two through nine of the hierarchical clustering of 

la ndf ailing hurricanes. 186 

C.l Comparison of plotting position formulae for N = 10 195 



LIST OF TABLES 

Number Page 

1 Hurricanes with central pressure < 982 mb, ranked in 

chronological order from 1900-84. Gulf coast United States 7 

2 Hurricanes with central pressure < 982 mb ranked in chronological 

order from 1900-84. East coast United States 14 

3 Miscellaneous Florida hurricanes with central pressure < 982 mb 

ranked in chronological order from 1900-1984 20 

4 Hurricanes with revised central pressure 2 6 

5 Forward speed of hurricanes and tropical storms for selected 

portions of the coast 32 

6 Initially selected coastal segments.. 35 

Results of Mann-Whitney test for a priori selection of coastal 

segments in the Gulf of Mexico.. 3 7 

8 Results of Mann-Whitney test for modified segments of the Gulf 

coast 38 

9 Percentages of variance accounted for by principal components...... 39 

10 Loading of hurricane parameters in the principal components which 

account for more than 12 percent of variance.... 39 

11 Coastal segments that include homogeneous hurricane parameters for 

the test of independence 41 

12 Breakpoint values for contingency tables 44 

13 Sample sizes of paired parameters of landfalling hurricanes for 

coastal segments 45 

14 An example of a general two-by-two contingency table 51 

15 Frequency of occurrence of different storm radii in two different 

class intervals of hurricane intensity observed in the Gulf of 

Mexico , 1900-84 52 

16 Severe hurricanes since 1900 with P Q < 93 mb 53 

17 Comparison of speeds of landfalling and alongshore storms for the 

vicinity of Charleston, South Carolina 61 

18 Partition of P q and for landfalling hurricanes striking the 

Atlantic coast south of 33.5°N , 64 



x i i i 



Number Page 

19 Selected landfalling hurricanes (1928-1983) used to estimate 

overland filling rates 113 

2 Changes in hurricane pressure deficits due to overland filling 117 

2 1 Summary sheet of information needed from this report for 

surge-frequency computations 12 8 

22a Summary sheet for Vero Beach, Florida 130 

22b Summary sheet' for 50 nmi north of Vero Beach, Florida 13 1 

22c Summary sheet for 50 miles south of Vero Beach, Florida 132 

23 Tropical cyclone parameters Vero Beach, Florida 13 4 

2 4 Data used in this report for probability analyses 137 

A.l Time, flight pattern, and flight level of NOAA/RFC missions into 

Hurricane David, September 1979 162 

A.2 Time, flight pattern, and flight level of NOAA/RFC missions into 

Hurricane Allen, August 1980 178 

C.l List of plotting position formulae 193 

C .2 List of plotting position formulae in the descending order of 

their p *s 194 

r m 



HURRICANE CLIMATOLOGY FOR THE ATLANTIC AND GULF COASTS 
OF THE UNITED STATES 



Francis P. Ho, James C. Su, Karen L. Hanevich, 
Rebecca J. Smith and Frank Richards 

Water Management Information Division 

Office of Hydrology 

National Weather Service 

National Oceanic and Atmospheric Administration 



ABSTRACT A climatology of hurricane factors important 
to storm-surge modeling is presented for the Atlantic 
and Gulf coasts of the United States. A smoothed 
frequency of hurricanes and tropical storms entering, 
exiting, and passing within 150 nmi of the coast 
during the period 1871-1984 is given. The central 
pressure and radius of maximum winds for hurricanes 
occurring during the 85-year period, 1900-84, were 
obtained from analysis of available hurricane data. 
Direction and speed of storm motion for hurricanes and 
tropical storms at the time they crossed the coast 
were also analyzed for the same 85-year period. The 
cumulative probability curves of each factor were 
plotted and analyzed for each 50-nmi interval along 
the coast. Selected probability levels of each 
distribution were summarized, and smoothed variations 
along the coast were obtained. Statistical 
independence of hurricane parameters has also been 
examined and interrelations of central pressure and 
radius of maximum winds investigated. 



1 . INTRODUCTION 

1.1 Authorization 

The National Flood Insurance Act of 1968, Title XIII, Public Law 90-448, 
enacted August 1, 1968, authorized and provides for a National Flood Insurance 
Program to insure residences and small businesses against hazard of damage or 
destruction by flood. The Federal Insurance Administration (FIA), a part of the 
Federal Emergency Management Agency (FEMA), is the executive agency for the 
National Flood Insurance Program. In July 1982 , a Joint Technical Assistance 
Work Plan was signed between FEMA and the National Oceanic and Atmospheric 
Administration (NOAA). The plan, among other things, allows for the National 
Weather Service (NWS), NOAA, to provide technical support Co FEMA upon request. 
Authorization for this particular study is Project No. 53967 under agreement 
No. EMW-84-E-1589 between the FIA, FEMA and the NWS, NOAA, dated March 15, 1984 
and duly signed April 2 5, 1984. 



1 .2 Purpose 

The Federal Insurance Administration, FEMA, requested the NWS, NOAA, to develop 
a comprehensive and authoritative set of hurricane clima tological statistics for 
the Atlantic and Gulf Coasts of the United States. These statistics are 
prerequisites in tidal flood-frequency analyses which are essential to establish 
flood insurance criteria for a given community. Coastal tidal inundations on the 
Gulf and Atlantic coasts of the United States are primarily caused by 
hurricanes. Therefore, the characteristics of these storms are the beginning 
point in making tidal flood-frequency analyses. The present study is a 
climatological assessment of the central pressure, radius of maximum winds, and 
other characteristics of hurricanes along the U.S. Atlantic and Gulf coasts in a 
manner suitable for determining the frequency of storm surge levels. It includes 
only the atmospheric characteristics of hurricanes and does not include surge 
levels that are the subject of other reports. 

The present study is an update and revision of an earlier study published as 
NOAA Technical Report NWS-15 (Ho et al 197 5), which will hereafter be referred to 
as TR 15. TR 1 5 presented a climatology of hurricane parameters important to 
storm-surge modeling along the U.S. Gulf and Atlantic Coasts. This climatology 
was an analysis of available hurricane data, with storm tracks from 1871 through 
1973, and also included data for other meteorological variables since 1900. 
TR 15 included the cumulative probability distributions of each hurricane factor 
analyzed at 50-nmi intervals along the coast, and smoothed variations of each 
factor at selected probability levels along the coast were presented. A smoothed 
frequency of tropical storms and hurricanes entering and exiting the coast as 
well as those storms passing within 150 nmi of the coast was also given in 
TR 15. The question of joint probability among the various factors was discussed 
qualitatively, but formal statistical tests were not considered in TR 15. 

The National Research Council of the National Academy of Sciences (NAS) 
reported on an evaluation of the FEMA Model for estimating potential coastal 
flooding from hurricanes (National Academy of Sciences 1983). This NAS report 
concluded that the basic approach used by FEMA is sound and appropriate for 
estimating 100-yr flood elevations in communities where severe flooding is caused 
by hurricane storm surges. However, the Advisory Committee of the NAS made 
several recommendations regarding the way in which coastal flood studies are 
conducted. The committee recommended, among other things, that the selection of 
storm samples and the adoption of appropriate interdependency assumptions should 
be carried out in a centralized way by an organization with the necessary 
expertise in hurricane climatology. The committee concluded that inter- 
dependencies among storm parameters, particularly among storm intensity, size, 
and direction, should be determined by that organization on a regional basis and 
an appropriate method for handling these interdependencies when applying the 
probability procedure to coastal flood elevations should be developed. 

1.3 Scope of Report 

The geographical region covered by the report is the U.S. Gulf and Atlantic 
coasts from Texas to Maine (fig. 1). The first objective was to define, clima- 
tologically, the frequency of hurricanes and tropical storms influencing each 
coastal segment. This was done for three classes of storms — those entering the 
coast from the sea (entering or landf ailing) , those having entered the coast and 
then proceeding from land to sea (exiting), and those moving parallel to the 



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Figure 1« — Locator map with coastal distance intervals marked (max). 

3 



coast, with the center remaining at sea, but within 150 nmi of the point under 
consideration (alongshore or bypassing). These frequencies are presented in 
Chapter 6. 

The second objective was to develop cumulative probability distributions for 
four hurricane parameters: (1) central pressure (P Q ), an index of storm inten- 
sity, (2) the radius of maximum winds (R), an index of storm size, (3) forward 
speed of the storm (T), and (4) direction of storm motion (9). Each of these 
factors influences the capability of the storm to produce storm tides. Chapter 2 
discusses in detail the data sources and analyses from which the hurricane 
characteristics were obtained. Probability distributions and their along-coast 
variations for each parameter are presented in Chapters 7 through 9 of this 
report. 

The statistical independence of hurricane parameters is considered in 
Chapter 3. The homogeneity of each parameter along the Gulf and Atlantic coasts 
was tested separately. Interrelations between pairs of parameters have been 
examined in Chapter 3. Non-linear relations between central pressure (P ) and 
radius of maximum winds (R) are discussed both dynamically and statistically in 
Chapter 4. For this purpose, the data base for P q and R was extended to include 
extreme hurricanes in the Caribbean and the Gulf of Mexico. Chapter 5 considers 
other conditional probability questions that are important to the currently used 
joint probability approach for tide-frequency analysis. 

Chapter 10 examines changes in the wind and pressure fields due to the filling 
of hurricanes overland. Finally, Chapter 11 discusses application of the results 
of this study to flood insurance studies. 

1.4 Relation to Flood Insurance Studies 

Meteorological parameters P R, 9 and T can be used together with other 
conditions as input to storm-surge models. Other conditions include boundary 
conditions such as bathymetry, orientation of the coastline, etc. A storm-surge 
model can be used to compute the surge heights at the coast. The storm surge 
generated by a hurricane is the increase of the sea water surface elevation due 
to two physical processes. One process is the water surface elevation increase 
in the core region of a hurricane where the atmospheric pressure is extremely 
low. This is the so-called "inverse barometer effect." The other process is the 
convergence of the sea water, driven by the surface wind from the deeper ocean to 
the shallower coastal regions. This is related to surface wind stress and 
bathymetry. The atmospheric pressure gradient in a hurricane is the difference 
between the central pressure and a peripheral pressure. The surface wind stress 
in a hurricane is parameterized on the basis of the wind field near the water 
surface. Using appropriate meteorological assumptions, a wind field can be 
derived from knowledge of the pressure gradient, the radius of maximum wind 
speed, and the forward direction and speed of the hurricane. 

The joint probability approach, as currently used in storm-surge frequency 
studies, assumes that each meteorological parameter used as input to the 
hydrodynamical model is independent. Development of storm-surge probabilities 
involves making computations for a range of meteorological parameters. The 
probability of occurrence of a given simulation is assumed to be the product of 
the probabilities represented by each input (meteorological) parameter. However, 
if the meteorological parameters are interrelated, a simple product of the 
individual probabilities is not appropriate. Hence, the need to evaluate the 



possibility of interdependence among the factors that are the focus of this 
study. With this specific application in mind, there were a number of decisions 
made during the course of our analysis that ensured that the results would be 
tailored to the needs of the hydrodynamic modeling application. Some examples 
include the selection of the radius of maximum winds at the time of minimum 
pressure, and the assumption that the parameters represented steady-state 
storms. But these decisions also mean that the "climatology" described in this 
report may not be appropriate for other more general meteorological applications. 

1.5 Previous Studies 

One of the first systematic compilations of the characteristics of hurricanes 
affecting the United States coast was Tropical Cyclones (Cline 192 6). Table 1 in 
Hydrometeorological Report No. 32 (Myers 1954) provided the first compilation of 
all hurricane central pressures and radii of maximum winds from 1900 to 1949. 
The National Hurricane Research Project Report No. 33 (Graham and Nunn 1959), 
hereafter referred to as NHRP 33, updated Myers' list and systematized the 
geographical distribution of the factors. Technical Paper No. 55 (Cry 1965) 
described all the hurricane tracks from 1871 to 1963, and cited the earlier works 
of this kind. HUR 7-97, Interim Report - Meteorological Characteristics of the 
Probable Maximum Hurricane, Atlantic and Gulf Coasts of the United States 
(Weather Bureau 1968) updated and revised the data in NHRP 33 and gave the 
geographical distribution of the characteristics of hypothetical hurricanes that 
had combinations of factors that made them the most severe hurricanes that can 
probably occur at a particular coastal location. NOAA Technical Report NWS 23 
(Schwerdt, et al 1979) revised and updated the previous studies on meteorological 
criteria for engineering design hurricanes. Neumann et al. (1981) extended the 
period covered in Cry's hurricane tracks and prepared revised tracks where 
additional data indicated that they were necessary. This provided a firm 
climatological base describing tropical cyclones on the synoptic scale. 

2 . DATA 

2.1 Introduction 

Observations from hurricanes occurring near the United States Gulf and Atlantic 
coasts were used in this study to determine probability distributions of various 
parameters. Data presented in this chapter are used in later chapters of this 
report. If additional data were required for a specific purpose, it is discussed 
in the chapter where required. 

The amount of observed data available from past hurricanes varies greatly and 
almost all of it required further analysis and interpretation before it could be 
of use for storm-surge computation. The amount of data available for any single 
storm also varies during different portions of the storm's life, from various 
geographic regions, and from different sections of the hurricane. These data are 
subject to numerous uncertainties in interpretation. We have attempted to bring 
this information together to make a comprehensive analysis, to develop accurate 
storm tracks from which speed and direction of storm motion are determined and to 
present an authoritative determination of central pressures and radius of maximum 
winds. Examples of detailed meteorological analyses are given in Appendix A. 



Tables 1 through 3, for hurricanes during the years 1900-84, list most of the 
information used throughout this report. Parameter values in the tables are given 
for storms with P Q less than or equal to 982 mb (2 9.00 in.) occurring within 
150 nmi of the Gulf and Atlantic coasts. The data are our update, revision and 
extension of Tables 1 and 2 in TR 15. There were a few changes made to the 
previously published data. In particular, to address the question of 
interdependence among parameters, available data were reviewed to ascertain their 
time of occurrence and to provide concurrent values of P and R where necessary. 

Tables 1 through 3 give the date at which a hurricane entered, exited or came 
closest to the coast. The point along the coast where the hurricane parameters 
may be applied is indicated in the tables as the coastal reference point. The 
tables list parameters for the 85-yr period, 1900-84. The year 1900 was chosen 
to initiate estimation of the parameters by weighing the inaccuracies that would 
result from the sparse data of earlier years against the desirability of a longer 
period. Each of the P and R values listed in the tables is followed by a 
superscript letter or letters that refer to a legend at the end of the tables 
giving the source of the data value. The storm direction, measured from the 
north, denotes the track direction from which the hurricane crossed or bypassed 
the coast. 

Tables 1 and 2 list a storm twice only if it crosses the coastline a second 
time (or if a bypassing storm makes another approach to the coast) after it has 
traveled a distance of 400 nmi (500 nmi along the Gulf Coast). An exception to 
this is Hurricane David: it was listed twice within 400 nmi, but only the second 
entry was included in the statistical computations discussed below. These dupli- 
cate storms are identified by a section mark (§) in the two tables. Hurricanes 
whose centers passed through the Florida Keys are listed in both the Gulf and 
Atlantic coast tables for the convenience of the user. The information on 
hurricanes which crossed the Florida Keys and eventually entered the west coast 
of Florida (within 500 nmi of its initial crossing), are listed separately in 
Table 3A. 

If a hurricane crossed the coast on one side of the Florida peninsula, with a 
P less than or equal to 982 mb (29.00 in.) and weakened in intensity to 
P greater than 982 mb when it was more than 50 nmi from the opposite coast, it 
was listed for only the initial coastline it crossed (table 1 or 2). Those 
exiting storms, still of hurricane intensity at, or within 50 nmi of, the coast 
of exit, are included in Tables 1 and 2. Hurricanes which entered the Florida 
coasts and moved northward over land maintaining hurricane intensity within 
50 nmi of the opposite coast are listed separately in Table 3B. They may be 
considered as bypassing hurricanes moving inland parallel to the coast. 

2.2 Sources of Data 

Original sources of hurricane data are barograph traces from land stations and 
ships, wind records from NWS and military stations, aircraft reconnaissance 
flight data, radar data, satellite data, miscellaneous pressure and wind reports 
and textual descriptions in the scientific literature. These descriptions have 
appeared in the Monthly Weather Review (published since June 1872), 
Clima tological Data, National Summary (since 1950), National Hurricane Research 
Project Report No. 39 (Graham and Hudson 1960), NOAA Technical Memorandum 
NWS SR-56 (Sugg et al. 1971), the book Tropical Cyclones (Cline 192 6), and a few 
other sources (e.g., data sources listed in append. A). 



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Tropical cyclone track information was used to determine the frequency of 
entering, exiting, and alongshore tropical storms and hurricanes, direction of 
forward motion and in some cases speed of motion. Smoothed best tracks have been 
given in several NOAA publications and periodicals previously cited. Cry (1965) 
combined data from available sources into a comprehensive report showing the most 
accurate and consistent locations of all tropical cyclones for the period 
1871-1963. These tracks were designed to provide a smoothed track for all 
storms. Neumann et al. (1981) have extended the period covered and prepared 
revised tracks where additional data have indicated they were necessary. In 
addition, Jarvinen et al. (1984) have prepared a computer file of North Atlantic 
tropical cyclones (commonly referred to as the HURDAT tape). This file contains 
dates, tracks, windspeeds, and central pressure values (if available) for all 
tropical cyclones that occurred during the period 1886-1983. This file is 
maintained by the National Hurricane Center (NHC), NOAA, in Miami, Florida and is 
updated annually. This data file contains storm positions and wind speed 
information at 6-hourly intervals. They are subject to some degree of 
uncertainty, especially for the earlier years. It should be noted that linear 
interpolation of the data within 6-hourly intervals could lead to inaccurate 
instaneous storm track and wind speed information. 

2.3 Hurricane Central Pressure (P Q ) Data 

The most important factor in storm surge modeling is the* intensity of the 
hurricane, which is directly related to its central pressure. Harris (1959) 
demonstrated that storm surge height is approximately proportional to the central 
pressure depression, other factors being constant. 

The specific pressure values in Tables 1 through 3 are the lowest pressures, 
generally determined from actual observations by either a barometer or 
dropsonde. For hurricanes of recent years, minimum pressure observed in 
penetrations of the hurricane eye by reconnaissance aircraft near the coast 
provided the central pressure in most cases. For earlier hurricanes, P values 
were estimated from observations taken at land stations. Observed pressures, P , 
were extrapolated inward to P (since P were rarely observed at the storm 
center) by using visually-fitted radial pressure profiles based on the formula 
(Schloemer 1954): 



P 
" - exp(-R/r) (1) 



P - P 
n o 



where P is the pressure at radius r, P 

is the pressure at some large distance from the center at which the profile is 

asymptotic, and R is the radius at which the windspeed is greatest. 

Schwerdt et al. (1979) computed pressure profiles for 19 past hurricanes using 
equation (1) and nine other pressure profile formulas and compared the results 
with observed data at radial distances of 40 and 80 nmi. They concluded that 
equation (1) gives a reasonably representative sea-level hurricane pressure 
profile. They also concluded that further refinements would not improve the 
reliability of the formula at this time because of the rather large scatter 
of pressure data around most hurricane profiles. 

23 



2.3.1 Central Pressure Criteria Based on Balanced Wind Model 

Tables 1 through 3 also list the lowest pressure observed at a station (P_), 
the observing station and a geographical reference to which P pertains (either 
at the coast or as far as 150 nmi offshore). The criterion used to select storm 
data for inclusion in Tables 1 through 3 ( P <_ 982 mb) was based on consideration 
of the windspeed computed from a balanced wind model (after Myers 1954): 



where, V Q = cyclostrophic windspeed, at which the centrifugal 

force exactly balances the horizontal pressure 
gradient force at radius, r, 

p = density of air, 

P = asymptotic pressure (same as defined in eq. 1), 



R = radius of maximum winds. 

At the radius of maximum winds (R=r), with a central pressure of 982 mb 
(29.00 in.) and an asymptotic pressure of 1015.9 mb (30.00 in.), the 
cyclostrophic windspeed is 73 mph, or about the windspeed required for 
classification as a hurricane. The asymptotic pressure used by Myers is 
different from the peripheral pressure suggested in Chapter 11. Both pressures 
are intended to be representative of the environment removed from the dynamics of 
the tropical cyclone; Myers' pressure is that value to which an exponential 
pressure profile defined by equation 1 is asymptotic. It is a parameter for 
defining the intensity of the pressure gradient and does not actually have a 
physical counterpart in the pressure field. The peripheral pressure used in this 
report is the surface pressure at the outer limit of a hurricane where the 
cyclonic circulation ends and, therefore, has a physical meaning. The 982-mb 
criterion was used to put a specific bound on the data sample. We realize that 
there have been storms with hurricane-force winds and central pressures higher 
than 982 mb south of 3 5°N. It is not intended to be used as a forecasting 
criterion to distinguish hurricanes from tropical storms. 

2 .3 .2 Central Pressure Adjustments 

In some areas, barometric pressures could not be obtained near the coast. The 
central pressures were determined at the location nearest the coast where 
reliable observations could be obtained and adjusted downward to a coastal 
value. This was done for those central pressures for which the lowest observed 
pressure was from a station inland or at a coastal station when the storm was 
emerging from land to sea. These adjustments were made for 13 hurricanes and 
were carried over from TR 15 and earlier reports, including NHRP 33. 
Recomputations using filling rates given in Chapter 10 did not show significant 
differences; P values for 3 of 13 hurricanes were revised. 



24 



Questions have been raised about the minimum central pressure of Hurricane 
Camille which struck the northern Gulf coast in 1969. The best obtainable value 
is needed because Camille had the lowest central pressure on the mainland coast 
since record keeping began during the later part of the last century, and 
stronglv influences the lower end of the probability distribution of central 
pressure. A minimum pressure of 905 mb was measured by an Air Force 
reconnaissance aircraft at 0016 GMT on August 17, 1969 near 25.2°N, 87.2°W, or 
250 mi southeast of the mouth of the Mississippi River. Eighteen hours later, 
and only a few hours before the center made landfall, another reconnaissance 
aircraft penetrated the hurricane, and reported an even lower central pressure of 
901 mb. A post-audit of the dropsonde computation at the National Climatic 
Center adjusted this to 908 mb. This value, which is quoted by Bradbury (1971), 
is the value in Table 1. The eye passed over Bay St. Louis, Mississippi, at 
landfall and an aneroid barometer a few blocks from the west end of the Bay 
St. Louis-Pass Christian bridge read 2 6.85 in. (909.4 mb) . This barometer was 
later checked and found to be accurate by the New Orleans NWS Office (DeAngelis 
and Nelson 1969). One may assume then that Camille remained in a near steady 
state during its last 25 hours at sea. 

2.3.3 Revised Central Pressure from Previous Studies 

A virtual absence of pressure data made it necessary to omit the Louisiana hur- 
ricane of August 6, 1918, in which the closest recorded pressure was some 
90 nmi from the path of the storm center. An estimate of P from such a 
distance would be highly questionable. Two hurricanes listed in NHRP 33 are not 
included in Tables 1 through 3. Upon reanalysis of the data, it was decided 
that both had weakened' to tropical storm strength before they reached a point 
50 nmi from where they exited the Florida coast. They are the storms of 
September 11, 1903 (Gulf coast) and October 20, 192 4 (Atlantic coast). 

On the basis of additional data discovered since the 1975 study, we revised 
the central pressure for several hurricanes. The most significant change 
involved the storm of September 20, 1909. The revision was based on a 
reconsideration of records available from the Weather Service Forecast Office in 
New Orleans. A few other changes of central pressures were made in hurricanes 
whose radius of maximum winds were revised. A recomputation using the pressure 
profile formula with the revised R values dictated these revisions. The dates of 
these hurricanes, and their previous and revised central pressure values are 
listed in Table 4. 

2.4 Hurricane Radius of Maximum Winds (R) Data 

Values of R for hurricanes were derived from various sources for the Gulf and 
Atlantic coasts of the United States. In TR 1 5 the values of R were for 
arbitrary locations and times. In this study, we reviewed all available data and 
determined concurrent values of P and R. The R values listed in Tables 1 
through 3 are derived near the location and time where P applies. With aerial 
reconnaissance data, the R values are obtained from wind data recorded during the 
same traverse of the storm center in which the minimum P was observed. In a few 
cases, R could not be obtained by any reliable method. Storms with R's in this 
category are represented in Tables 1 through 3 by the abbreviation MSG (missing). 



25 



Table 4. — Hurricanes with revised central pressure 







Gulf 




Previous 


Revised 


Date 




P o 


P o 






(mb) 


(mb) 


Oct. 18, 1906 




976.6 


966.8 


Sept. 20, 1909 




980.0 


965.1 


July 5, 1916 




961.1 


950.2 


Nov. 5, 193 5 




972.9 


977.0 


Oct. 5, 1948 




977.0 


962.7 


Sept. 10, 1960 


(Donna) 


933.0 


93 0.0 


Sept. 15, 1960 


(Ethel) 


972.0 


976.0 



Date 



Atlantic 
Previous Revised 














( 


3 










(mb) 


(ml 


O 


Sept. 


17, 


1906 




981.4 


976 


.6 


Sept. 


18, 


1926 




93 4.3 


93 1 


.0 


Aug. 


23, 


1933 




969.5 


966 


.5 


Sept. 


21, 


1938 




939.7 


943 


.0 


Sept. 


15, 


1944 




958.7 


955 


.3 


Sept. 


17, 


1947 




940.1 


946 


.8 


Aug. 


28, 


1958 (Daisy) 


957.0 


949 


.0 


Sept. 


12, 


1960 


(Donna) 


961.1 


959 


.0 


Sept. 


10, 


1964 


(Dora) 


965.8 


961 


.0 



2.4.1 Source of Radius of Maximum Winds 

The values of R in the tables were developed from several sources: 1) windspeed 
records from aerial reconnaissance (for hurricanes since 1947), 2) windspeed 
records from land stations, whenever applicable, 3) approximations of eye radii 
deduced from airborne or land-based radar, 4) computations from an estimate of 
the pressure profile, or 5) on the basis of narrative or tabular data in the 
Monthly Weather Review. 

2.4.1.1 Radius of Maximum Winds from Aerial Reconnaissance. Maximum flight- 
level winds and estimated maximum surface winds are usually included in flight 
reports from reconnaissance aircraft. Flight-level winds, recorded at one-second 
intervals by N0AA research aircraft flown into hurricanes have also been 
available since 1953. Recorded flight-level winds were processed and 10-second 
averages are stored on microfilm for data prior to 1973 and on magnetic tapes for 
recent years. Wind and pressure data on microfilm were tabulated, plotted, and 
analyzed for hurricanes affecting the U.S. coasts. From magnetic tape records 
since 1973, composite maps of flight-level winds relative to the storm center at 
given intervals and winds at various radial distances from the storm center 
recorded in a traverse through the eye were plotted by computer and made 
available to us by the Hurricane Research Division (HRD) of the Atlantic 
Oceanographic and Meteorological Laboratory (AOML) of NOAA. Analyses of these 
maps yielded another measure of the radius of maximum winds. Examples of these 
analyses are given in Appendix A. 

It is generally accepted that, above the boundary layer, there is little 
vertical shear in a hurricane windfield in the lower troposphere (below about 
600 mb). Miller (1958) developed a 3-dimensional description of the windfield in 
a tropical cyclone. Shea and Gray (1972) found that only the weaker storms 
exhibit a tendency for a slope of the radius of maximum winds with height; more 
intense storms do not. Willoughby et al. (1982) analyzed multi-level (1,500, 
5,000 and 10,000 ft) flight data in Hurricane Allen (1980) and showed that 



26 





50 




45 




40 




35 


^ 




- 


30 


'"' 




o 




LkJ 


RS 


■jA 




.n 






20 


2 












3 


15 




10 




OBSERVED WIND SPEED 



3 



00 



OS 



i 2 



00 



00 



TIME CGMT5 
7igure 2. — Hourly observations of wind speed and direction, and distance of 
Allen's center from Brownsville, Texas for period 1300 GMT on August 8 through 
0600 GMT on August 11, 1980. 

the magnitudes of the maximum winds at different flight levels were generally 
quite similar. We concluded that flight-level wind data recorded at altitudes 
below the 600-mb level can be used to determine the surface value of R in 
hurricanes of moderate or greater than average intensity. Examples of this 
method of obtaining R are given in the data analysis in Appendix A. 

2.4.1.2 Radius of Maximum Winds from Wind Records. Observed maximum winds are 
determined by noting the time when a wind-reporting station experienced the 
highest windspeed prior to the wind slackening in the hurricane's eye. From a 
knowledge of the location of the storm center at that time, one can deduce a 
value of R. Similar results can be obtained from various types of wind 
recorders. The windspeeds read off anemometer records were plotted on a time 
scale and a smooth curve drawn. A curve of distance from the storm center, as 
measured from the best track, was constructed on the same time scale. The two 
curves are shown for Hurricane Allen (1980) in Figure 2. The two peaks in the 
wind graph indicated that the storm's track took the center closer to the station 
than the radius of maximum winds. The 'observed' radius of maximum winds would 



27 



be the distance from the wind center at the time of these peaks. If the track 
had kept the storm center beyond R, there would have been only one peak in the 
wind profile. In this case, it was established that the radius of maximum winds 
was less than the distance of station from the storm track. 

2.4.1.3 Radius of Maximum Winds from Eye Radius. In their work, The Structure 
and Dynamics of the Hurricane's Inner Core Region , Shea and Gray (1972) stated 
that, in the mean, the radius of maximum winds occurs at radii 5 to 6 nmi outside 
the inner radar eye radius (IRR) - assumed synonymous with the inner cloud 
wall. The IRR may be obtained from land-based radar, ships at sea, or 
aircraft. Figure 3, taken from Shea and Gray, shows the position of R relative 
to the IRR for 2 1 Atlantic Ocean and Gulf of Mexico hurricanes. Figure 4, also 
from Shea and Gray, shows the difference between R and IRR versus the maximum 
windspeed for radial flight legs. Note that the more intense the wind the better 
the agreement between R and IRR. 

2.4.1.4 Radius of Maximum Winds from Pressure Fit. Computed R's can be 
estimated by fitting an exponential pressure profile to the data from a given 
hurricane. By their nature, computed values of R are more subject to error than 
observed R's. The procedure was used in previous studies to derive estimates 
that were carried over into the present study and was discussed by Myers (1954). 

2.4.1.5 Radius of Maximum Winds from Monthly Weather Review . Reports of radii 
of maximum winds extracted from storm analyses in the Monthly Weather Review 
usually consist of estimates of the diameters from the measured time interval 
between the slackening and resumption of hurricane-force winds over some 
point near or along the coast. In other instances, researchers have reported 
their findings in the Monthly Weather Review , and these results (including 
estimates of the radius of maximum winds) have been accepted by the authors of 
this study. 

2.5 Speed (T) and Direction (9) of Forward Motion 

The translation speed and direction of hurricane motion are, among others, 
important factors for determination of storm surges along the open coast. 
Forward speed and direction were determined primarily from analysis of hourly 
hurricane positions when they were available. Generally, the analyses of 
meteorological data are weighted toward synoptic-scale motions. The hurricane 
track, thus obtained, is a best estimate of the large-scale storm motion and not 
a precise location of the eye at discrete time intervals. In this report, 
direction of storm motion is measured clockwise from north and denotes the 
direction from which the storm crossed or bypassed the coast. 

2.5.1 Source of T and 8 Data 

The T and 9 information in Tables 1 through 3 were extracted from storm track 
charts. Hurricane tracks compiled by Cry (1965) and the charts for recent years 
published by the NHC, NOAA, in Miami, Florida (Neumann et al. 1981, and Jarvinen 
et al. 1984) were used. The speeds were derived mostly from detailed track 
charts, depicting hourly or bi-hourly positions in the vicinity of the coast, 
such as: Myers (1954), Graham and Hudson (1960), and Ho and Miller (1982, 
1983). The listed T and 8 pertain to the time of landfall, exit, or closest 
approach to the coast. In Tables 1 through 3, both the T and 9 data prior to 
1973 were carried forward from Tables 1 and 2 of TR 15. 

28 




Figure 3. — Radius of maximum winds (R) versus inner radar eye radius (IRR). 
Points falling on the 45° line are Chose where the R and IRR coincide- The 
curved line indicates the best fit curve (from Shea and Gray 1972). 



a: ic- S 



I 










' • 




- 1 






• 








- 1 








• 






< 




• 


• 


• 






i*i 








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• 


: 












• • 


• 




— d 








• • • • • 






_ UJ 






• 


9 • 


• 




£; 




•• 




•••••• • 


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• • 


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• ••• • 




•/) 








• 


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v* 


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•• • • / •• • 




2 










• • • 




X 


• • • 


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• 




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IRR 




_ 












- 








• • 


• • • . • 





30 SO ICC 

MAXIMUM WIND SPEED ! 



Figure 4. — Difference between the radius of maximum winds (R) and the inner radar 
eye radius (IRR) versus maximum wind speed. The best fit curve is indicated by 
the heavy line (from Shea and Gray 1972). 



29 



2.5.2 T and 9 Data Used in Probability Distributions 

In our present study, cumulative probability curves for T and 9 were plotted 
for tropical cyclones since 1900. In TR 15, T data for hurricanes since 1886 
were used in the plots. We made similar analyses using hurricane data from 1900- 
84 and found little difference in the results. 

To expand our data sample for speed of forward motion, we utilized T data from 
all tropical cyclones landfalling on the Gulf and Atlantic coasts. In addition 
to the T data for landfalling hurricanes listed in Tables 1 through 3, average 
speeds for weaker storms were estimated from 6-hourly positions given on the 
HURDAT tape (Jarvinen et al. 1984). We chose the average speed, computed at 
synoptic hours, closest to the time of landfall as an approximation for 
landfalling tropical storms. 

Directions of landfalling tropical cyclones were determined at the times they 
crossed the coast. In TR 15, the sample of 9 included values from hurricanes and 
tropical storms since 1871. In the present study, 9 data came from tropical 
cyclones that occurred during the 85-year period, 1900-84. 

3. METEOROLOGICAL PARAMETERS AND THEIR INTERRELATIONS 

3.1 In t r oduc t ion 

Meteorological parameters used in the hurricane climatology analysis are 
central pressure (P Q )> radius of maximum winds (R) , forward speed (T) and 
direction (9) of storm motion. Since the computation of storm-surge frequencies 
using the joint probability approach assumes independence among the parameters, 
any interdependencies must be identified and taken into account. 

In addition to the basic hurricane parameters, location parameters include a 
coastal reference milepost (m), the latitude (0) and the longitude (X). The 
mileposts are assigned such that m = at the Mexican border and increases along 
the Gulf coast toward Florida, reaching a value of 1415 at the southern tip of 
Florida. The value of m further increases northward along the Atlantic coast to 
m = 3100 at the Canadian border (see fig. 1). 

3.1.1 Overview of the Statistical Study 

The ultimate purpose of the statistical tests was to find interrelations 
between the hurricane parameters, if any, so that those parameters could be 
properly accounted for in the storm-surge frequency computations. Because of 
large natural variability, our data sample did not provide a sufficient number of 
storms to estimate the underlying populations over coastal segments short enough 
to allow homogeneity to be assumed a priori. This made it desirable to pool data 
over as large an area as possible, to increase reliability of population 
estimation and hypothesis testing. However, the pooled data could only include 
coastal segments that were both statistically and meteorologically homogeneous. 
While determination of meteorologically homogeneous coastal segments was, of 
necessity, somewhat subjective, we complemented our judgments with consideration 
of statistical homogeneity. We felt that the variability in the data and limited 
sample sizes precluded a purely statistical determination of homogeneous regions. 



30 



The statistical methods used in this chapter are outlined in Appendix B, 
wherein the rationale for their choice, their limitations, and the interpretation 
of the results are discussed. We used two methods to delineate regions in which 
the hurricane parameters might be considered homogeneous: a meteorologically 
based method and a statistical method (based on cluster analysis). 

For the meteorological method, hurricanes that struck a coastal segment that 
had relatively uniform orientation were grouped together. We then performed 
tests to determine whether the statistical characteristics of hurricane 
parameters among the various groupings were similar. The groups with no 
significant differences in statistical characteristics were considered for 
combination into a larger group. These pooled groups provided larger sample 
sizes for tests of interrelations between hurricane parameters. 

We also performed a cluster analysis on the parameters of all hurricanes 
located along Gulf and Atlantic coasts; the hurricanes were separated into 
clusters (groups) based upon the characteristics of the sample data. The groups 
of hurricanes so obtained were then examined using principal component analysis 
and discriminant analysis to determine whether significant differences existed 
between the groups. The results were compared with those of the meteorological 
method. 

3.1.2 Scope of the Chapter 

In Section 3.2, a comparison of the statistical characteristics of forward 
speed of hurricanes and tropical storms Is discussed. Practical problems with 
the treatment of the direction of motion of landf ailing hurricanes and tropical 
storms is also discussed in this section. The homogeneity of hurricane 
parameters from different geographical regions is discussed in Section 3.3. The 
results of homogeneity test were used as guidelines for pooling the data samples 
used in the independence tests. In Section 3.4, interrelations between hurricane 
parameters are examined. In Section 3.5, the interdependence between hurricane 
parameters is discussed, and our conclusions are presented. 

3.2 Considerations of Data Samples for Statistical Tests 

Tropical storm data included forward direction and speed for the Gulf and 
Atlantic coasts of the United States. Central pressure and radius of maximum 
winds for individual tropical storms could not be adequately specified. However, 
central pressures of all tropical storms are, by our definition (see sec. 2.3.1), 
greater than 982 mb. Only landfalling tropical storm data were considered. 

The landfalling tropical storm data were separated into two groups: one for 
the Gulf coast and the other for the Atlantic coast. For comparison, the 
landfalling hurricane data were also separated in the same manner. To examine 
whether the distributions of landfalling hurricanes and tropical storms should be 
considered separately, we set up the following data subsets: 

GH: landfalling hurricanes on the Gulf coast, 

GT: landfalling tropical storms on the Gulf coast, 

AH: landfalling hurricanes on the Atlantic coast, and 

AT: landfalling tropical storms on the Atlantic coast. 



31 



Table 5. — Forward speed of hurricanes and tropical storms for selected portions 
of the coast 

Type of Sample Average Speed ~ Standard Deviation 

Storms "Size (kn) (kn) 

___ West coast of Florida (1050 <_m <1415 nmi) — 

Hurricanes 13 10.5 " 3.6 

Tropical storms 28 15.8 7.6 

Northern Atlantic coast (m > 2 400 nmi) 
Hurricanes 7 34.7 7.8 

Tropical storms 12 22.8 6.7 

We performed the (1) Mann-Whitney test, (2) Wilcoxon two-sample test with 
normal approximation, and (3) Kruskal-Wallis test with Chi-square approximation 
on the data set pairs GH and GT, and AH and AT. Part of the Mann-Whitney test, 
and all of the Wilcoxon and Kruskal-Wallis tests were conducted using SAS 
procedures. 

3.2.1 Forward Speed 

The results of the three tests show no significant difference between the 
distributions of landfalling hurricanes and landfalling tropical storms for 
either the Gulf or Atlantic coasts. We also inspected scatter diagrams of 
forward speed vs. railepost for landfalling hurricanes and landfalling tropical 
storms. Figures 5a and 5b show that the distribution of forward speed of 
landfalling hurricanes and tropical storms for the west coast of Florida 
(m = 1050-1415) differs from that for mileposts greater than. 2400. The latter is 
located north of Chesapeake Bay. Table 5 shows that tropical storms that struck 
land, on average, moved faster than did hurricanes along the west coast of 
Florida, but moved more slowly than hurricanes for the northern portion of 
the Atlantic coast. The variation along the Florida coast appears to be 
reasonable, and is explained by the fact that storms that recurve tend to move 
faster as they become embedded in stronger westerly flow. Strong westerlies also 
tend to disrupt the delicate thermal circulation necessary to support intense 
storms. Therefore, storms that recurve tend to be weaker (tropical storms) 
and move more rapidly. We concluded that hurricanes and tropical storms in this 
area represented complementary portions of the same distribution, not separate 
distributions. 

Clearly, the observations north of milepost 2 400 cannot be explained this 
way. While we have no fully satisfactory explanation for what the data indicate, 
we note that the sample size is rather small, and for the hurricanes, the 
variability is considerably higher than the Florida sample (see table 5). 
Furthermore, most storms, whether hurricanes or tropical storms, that reach 



SAS is the Statistical Analysis System. Mention of a commercial product does 
not constitute endorsement by the Federal Government. 

32 




050 1100 1200 1300 I 400 "500 



MILEPOST Cnmi) 



* Hurricanes 

• Tropical Storms 





30 


- 




— r 




# 


> i i 


r- T" " r 1 






1 1 

(b) 




40 












* 






* 


- 




30 


- 




• 




* 
* 




• 






• 


a 

LU 
Q. 


20 

10 




" 


• 




* 
• 




• 
• 


• • 


• 




• 



2400 2500 



^ Hurrfeanvt 

• Trojteal 3torm« 



2600 2700 2800 2900 

MILEPOST Cnmi) 



3000 3100 3200 



Figure 5. — Forward speed of landfalling hurricanes and tropical storms versus 
adlepost (a) along the Gulf coast of Florida, and (b) along the Atlantic coast. 



33 



these northern latitudes are moving quite rapidly. They appear to have been 
transformed into systems whose circulations have extratropical characteristics. 
The fastest moving storms are probably propagating as waves along a baroclinic 
zone. Because of the small sample size, the generally large variability and the 
indication that the dynamics of the storms north of milepost 2400 appear to be 
quite unlike classical tropical cyclones, we exercised judgment in our analysis 
of these data. We felt that the best estimate of the underlying population could 
be achieved by consideration of the forward speed of both hurricanes and tropical 
storms. Based upon the test results and on our judgment, we treated the speed of 
motion for tropical storms the same as for hurricanes for both the Gulf and 
Atlantic coasts. 

3.2 .2 Forward Direction. 

The data only include landf ailing storms. In our data sample, landf ailing 
hurricanes outnumber hurricanes in the other categories (bypassing and exiting) 
by a large amount. The sample sizes in the bypassing and exiting categories are 
so small that it would not be possible to make meaningful inferences based on 
statistical analysis. 

Landfalling tropical cyclones are defined as those that strike the coast, hence 
their range of forward directions is limited by the coastal orientation. The 
range of directions can vary greatly as the coastal orientation changes over 
short distances. This variation can limit the range of directions in the 
category of landfalling storms in a way totally unrelated to real meteorological 
variability. For this reason, we decided that it was not appropriate to treat 
direction of motion as a random variable for the purposes of hypothesis testing, 
and in particular, for examination of interrelations with other parameters. 
Possible interrelations between 9 and the other hurricane parameters will be 
considered further in Chapter 5. 

3.3 Homogeneity of the Hurricane Data Samples 

For the purposes of this study, homogeneity for a given coastal segment means 
that parameter estimates from a sample of storms for one location appear to be 
drawn from the same population as the parameter estimates for any other location 
in the segment. 

We separated the storms into groups so that each group consisted of the storms 
that made landfall on a coastal segment that had relatively uniform orienta- 
tion. Presumably, if the segment was properly selected, the data would be 
meteorologically homogeneous. We then performed statistical tests to determine 
whether the frequency distribution of the parameters from one group appeared to 
be the same as other groups. The groups which appeared to show no significant 
difference in their distributions were considered for combination into a larger 
group. 

Cluster analysis of the parameters provided another method to separate the 
hurricanes into groups based on the characteristics of the data sample. The 
groups of storms so obtained were tested using principal component analysis and 
discriminant analysis to determine whether they appeared to be reasonable 
partitions. The results were then compared with those of the meteorological 
method (based on coastal orientation). 



34 



Table 6. — Initially selected coastal segments 



Segment 
Number 



Number of Milepost Range 
Hurricanes (smoothed coastline) 



Description 



23 



0-400 



Gulf coast from Mexican 
border to Galveston, Texas 



400-700 



700-1100 



Gulf coast from Galveston, 
Texas to Mississippi delta 

Gulf coast from Mississippi 
delta to Suwannee Sound, 
Florida 



12 



1100-1415 



Gulf coast from Suwannee Sound, 
Florida to the southern tip of 
Florida peninsula 



1415-1800 
1800-2200 



Whole Atlantic coast of Florida 

Atlantic coast from Georgia to 
Cape Hatteras 



22 00-2 700 
2 700-3100 



Atlantic coast from Cape 
Hatteras to Rhode Island 

Atlantic coast from Rhode Island 
to Canadian border 



3.3.1 Methods for Testing the Homogeneity of Storm Parameters 

In the meteorological method, we first selected eight segments along the Gulf 
and Atlantic coasts of the United States. These eight segments were located in 
the milepost ranges shown in Table 6 and are shown schematically in Figure 6 (see 
also fig. 1). The number of landf ailing hurricanes in each segment is also 
listed in Table 6. 

There were four segments on the Gulf coast and another four segments on the 
Atlantic coast. Milepost 1415 is located at the southern tip of Florida. Along 
each segment, the orientation of the coastline is relatively uniform, except for 
the two most northern segments along the Atlantic coast. For the first six 
segments we used the Mann-Whitney test to examine the relation of P , R, and T 
among pairs of segments. Segments 7 and 8 were not included in the testing 
because of the small numbers of observations. The test was used to determine 
whether the distribution functions of a given parameter appeared to be 
significantly different between two segments of the coastline. If no difference 
in distribution functions for two segments was detected for all parameters, those 
two segments could be combined if the meteorological conditions in each segment 
were deemed to be similar enough. 

The seven parameters used in the cluster analysis were P , R, 0, T, the 
milepost value (m), the latitude (0), and longitude (A) of the landfalling 
point. For each grouping, principal component analysis and discriminant analysis 



35 



1 I I 1 [ 1 I I 1 I 1 1 I I 

GULF COAST 



I I I | J I I I 
ATLANTIC COAST 



Ml! 



12 3 4 5 6 7 8 



COASTAL SEGMENTS SELECTED INITIALLY 


























RESULT OF MAM-WHITNEY TEST 



1 




4 


| 




2 




3 


|lllll 


5 


illiij 




!*: : 




t$ 














&**>**&:'] 



RESULT OF CLUSTER ANALYSIS (? , R, 9 , T , n, , k ) 

o 





' 


> 


1 


\ \ 













LOCATIONS OF FREQUENCY MINIMA 



GLF C ATL A 






COASTAL SEGMENTS SELECTED FOR INDEPENDENCE TESTING 
GULF COAST | ATLANTIC COAST 

t I 1 I I I I 1 I I 1 1 1 I 1 1 1 1 1 I I I 1 I I 1 1 



I I 



5 10 15 20 25 20 

MILEPOST (100 nmi) 

Figure 6, — Possible homogeneous regions for landf ailing hurricane parameters. 
Shaded areas have Insufficient or no data. 



36 



Table 7. — Results of Mann-Whitney test for a priori selection of coastal segments 
in the Gulf of Mexico 



Segment Segment Number 

Number 12 3 



Segment Number 
1 2 3 



Segment Number 
1 2 3 



* 

* * 



* 



* 



Segments as given in Table 6 

* indicates segments with similar distributions 

indicates segments with different distributions 



were used to examine the similarity between the groups. The most distinctively 
separated groups were selected and the parameters within each group were examined 
for possible interrelations. 

3.3.2 Comparison of Results from Different Homogeneity Tests 

3.3.2.1 Meteorological Method. After the coastal segments were selected 
(table 6), the Mann-Whitney test (Conover 1971) was performed to compare pairs of 
segments. Adjacent segments with no significant difference in distribution 
functions were considered for combination. 

The results for the Gulf coast are shown in Table 7. In all cases, adjacent 
segments appeared to have similar distributions. However, for P and T, some 
segments that were separated by one or two segments appeared to come from 
different distributions. For instance, for both parameters, segments 1 and 3 had 
different distributions, even though they both had distributions similar to that 
of segment 2. To explore the variation along the Gulf coast further, we divided 
the data sample into different segments. An example is shown in Table 8, where 
only 3 segments were used. Again, all segments appeared to have similar 
distributions of R, but different distributions of P and T. Our analysis of 
shifting the segment boundaries led us to conclude that the data appear to be 

Table 8. — Results of Mann-Whitney test for modified segments of the Gulf coast 



Segment 
Number 


P 
o 
Segment Number 

1 2 


R 

Segment Number 

1 2 


T 

Segment Number 

1 2 


Milepos t 
Range 


1 
2 
3 




* 


* 

* * 




* * 


0-500 
500-1000 
1000-1415 



* indicates segments with similar distributions 
indicates segments with different distributions 



37 



"locally homogeneous." It appears that there may be variations along the 
smoothed coastline in the Gulf that could result in samples that would not be 
homogeneous if the segments were too large. However, it is not clear what "too 
large" is. By that, we mean that the variation appears continuous and that 
there are no obvious breakpoints between homogeneous regions. Therefore, the 
data can be considered homogeneous locally. In Section 3.3.3, we combine this 
with an evaluation of the statistically based cluster analysis to specify 
homogeneous segments for the independence testing. 

The concept of local homogeneity was also assumed to apply for the Atlantic 
coast. As indicated in Table 6, the number of storms beyond milepost 2200 was 
too small to consider formal statistical testing. The results of the Mann- 
Whitney test for the region south of milepost 2200 were variable, depending on 
the segments chosen. However, the results were not inconsistent with the concept 
of local homogeneity. This Is reasonable, considering the known variation of the 
hurricane parameters with latitude. 

3.3.2.2 Cluster Analysis. The results of the cluster analysis were generally 
consistent with the results of the meteorological method. In application of the 
cluster analysis procedure, the number of clusters was assigned a priori, and the 
cluster boundaries were then determined. Analyses for two through nine clusters 
were conducted. When five clusters were selected, the partitioning was most 
similar to that determined by the meteorological method. The cluster analysis 
technique assigns each storm to a particular cluster and assigns it an 
identification (ID) number. These ID numbers are shown in the schematic in 
Figure-6. Somewhat surprisingly, each of the clusters included storms that 
struck land over a continuous extent of the coast. That is, milepost alone could 
be used to totally delineate which storms were included within each cluster. 
This is consistent with our judgment used in specifying regions by the 
meteorological approach (sec. 3.3.2.1). The cluster boundaries for the 
five-cluster partition were generally located in regions of storm-frequency 
minima (see fig. 27). Because of this, the last storm in one cluster (largest 
milepost value) could be at a considerable distance (40 nmi or more) from the 
first storm in the adjacent cluster. With this in mind, a cluster boundary in 
Figure 6 should be considered a point somewhere in the transition region - 
cluster boundaries are not precise delineations. 

3.3.2.3 Discriminant Analysis. To determine how well the clusters of hurricanes 
were separated, discriminant analysis was performed on them. In addition to 
providing the seven parameters mentioned in Section 3.1 (P , R, T, 9, m, 4>, A), a 
cluster identification number (as shown in fig. 6, for a 5-cluster partition) was 
also used as input to the procedure. The results showed that hurricanes were not 
distinctively separated by the cluster analysis for 3 through 9 clusters. For 
example, in the case of five clusters, Hurricane Hazel of 1954, which made 
landfall at milepost 2 077, was put in cluster 3 by the cluster analysis but 
classified into cluster 1 by the discriminant analysis. In this case, cluster 1 
includes hurricanes which made landfall in the milepost range 1-500 and cluster 3 
includes those in the milepost range 1752-2294. The discriminant analysis and 
the cluster analysis agree only on classifying all landfalling hurricanes into 
two clusters: one Includes those in the milepost range 1-1201 and the other in 
the milepost range 12 92-2 750, with missing data outside of these ranges. However, 



38 



Table 9. — Percentages of variance accounted for by principal components 

Cumulative 

Principal Percentage Percentage 

Component of Variance of Variance 

1 44.6 44.6 

2 15.2 59.8 

3 14.3 74.1 

4 12.2 86.3 

5 9.0 95.3 

6 4.5 99.8 

7 0.2 100.0 



examining these milepost ranges, we felt that these two clusters cannot be 
meteorologically homogeneous, especially the second cluster, because it includes 
hurricanes which are generally larger in size and faster in forward motion as 
compared to hurricanes in the lower latitudes. 

3.3.2.4 Principal Component Analysis. Principal component analyses were 

conducted to examine the relative importance of the parameters. The percentage 
of variance that each principal component accounted for is shown in Table 9. The 
first principal component accounts for almost 45 percent of the total variance, 
and each of the next three principal components account for more than 12 percent 
of the total variance. "Loadings" provide a measure of the contribution of the 
parameters to each component. The loading of the hurricane parameters in the 
four most significant principal components is shown in Table 10. Each column in 
the table is an eigenvector normalized to have a unit length. This means that 
the square root of the sum of squares of numbers in each column is unity. 
Table 10 shows high positive loadings on the milepost (m) and landfalling 
latitude (0) and high negative loading on the landfalling longitude (A) in the 
first principal component, and high positive loading on central pressure (P.) in 
the second principal component. The loading and importance of the first 

component confirms our meteorological judgment that location is an important 
factor in delineating homogeneous regions. 

Table 10. — Loading of hurricane parameters in the principal components which 
account for more than 12 percent of variance 

Principal Component 
Parameter 12 3 4 

" F 07l3 0787 =0TT4 -0.16 

R 0.31 0.33 0.11 0.60 

9 0.20 0.13 0.73 -0.57 

T 0.39 -0.28 0.39 0.26 

-0.2 1 
0.25 
0.34 



0.13 


0.87 


-0.14 


0.31 


0.33 


0.11 


0.20 


0.13 


0.73 


0.39 


-0.2 8 


0.39 


0.50 


-0.14 


-0.38 


0.47 


0.01 


0.11 


•0.48 


0.14 


0.3 6 



39 



■ I . 

2 

■3 



* 


t 


ii 


, ! 


1 


1 


* 


<t««2 » 




3 


























1 












3 










3 












i 










"» 


• » 2 








3 


3 


3 










; 






1 


1 


... .- 


% 


-h._?:!\ 




3 










3 




3 


3 




: 




1 








2 


"»Ji 


3 




















. 












2 


212 


• »a » 






3 










3 


















2 2 


2 


























♦ 




i 










• 




















33 





-3.6 



•2.4 



.2 



0.0 



1.2 



2.4 



3.6 



4.8 



Figure 7. — Plot of the second principal component versus the first principal 
component. Each symbol represents a landfalling hurricane and indicates Che 
cluster to which it belongs. 

Using the classification provided by the cluster analysis, the second principal 
component was plotted versus the first principal component as shown in 
Figure 7. In this graph, each symbol represents a landfalling hurricane and the 
symbol indicates the cluster to which it belongs. The figure shows that 
clusters 1, 3, and 5 are distinctively separated with few "misclassif ications," 
and clusters 2 and 4 are mixed. Cluster 2 includes landfalling hurricanes in the 
milepost range 1292-1584 which covers the southwest and southeast Florida 
coast. Cluster 4 includes landfalling hurricanes in the milepost range 560-1201 
which covers the Gulf coast from eastern Louisiana to the Florida panhandle. 
Thus the landfalling hurricanes in the milepost range 560-1584 are difficult to 
classify into distinctive subgroups on the basis of principal component 
analysis. Note that location parameters played an important role in the first 
component, and ? in the second component (see table 10). Figure 8 is a scatter 
diagram showing the distribution of ? as a function of milepost for clusters 2 
and 4. While there are fewer landfalling storms for mileposts 1000-12 50, the 
range of pressures does not indicate any obvious clustering. In both the western 
and eastern portions, most P 's range upwards from 930 mb, with an intense storm 
in each section. It seems reasonable to group these data together on the basis of 
the characteristics of their pressures. 

3.3.3 Selection of Hurricane Groups for Independence Testing 

The fact that the location parameters play an important role both in the prin- 
cipal component analysis and in the cluster analysis supports our use of coastal 
segments for the delineation of homogeneous regions of hurricane parameters. Con- 
sideration of meteorological factors and the results of the statistical analysis 
suggest boundaries between milepost 400-700, 1000-1200, 1600-1800, 2200-2300 and 
near 1415. Milepost 1415 is chosen as a boundary because it is a dividing point 
between the Gulf and Atlantic coasts. Tne regions we ultimately judged to be 
homogeneous are summarized in Table 11 (see also fig. 6). 



40 



Table 11.— Coastal segments that include homogeneous hurricane parameters for the 
test of independence 



Segment 

ID 



Mile post 
Range 



Description 



GLF 


A 


0-4 50 


GIF 


3 


450-1050 


GLF 


C 


1050-1415 


ATL 


A 


1415-1800 


ATL 


B 


1800-2 300 


ATL 


C 


2300-3 100 



Texas coast 

Gulf coast from Louisiana to Florida Panhandle 

West coast of Florida south of 30°N 

East coast of Florida 

Atlantic coast from Georgia to North Carolina, 

including Cape Hatteras 
Atlantic coast from Virginia to Canadian border 






•• 



900 1 000 ! 1 00 1 200 

MIL£P0ST CnmiD 



Figure 3.— Central pressure of landfalling hurricanes versus atLlepost. 



41 



3.3.3.1 Gulf Coast. Both our meteorological judgment and statistical analyses 
suggested that the region along the coast of Texas could be considered meteoro- 
logically homogeneous. Our initial boundary was at milepost 400 and the analyses 
in Sections 3.3.2.2 through 3.3.2.4 suggested a break near milepost 500. Since 
the Gulf coast turned most sharply around milepost 450, we decided to select this 
point to delineate our first homogeneous region. We had initially divided the 
south-facing portion of the Gulf coast (mileposts 400-1100) into two portions, 
with the break near the Mississippi delta (milepost 700). We did this to 
consider the possibility that storms affecting the eastern and western portions 
might be different. The results of the statistical analysis did not support this 
division. The statistical analysis suggested extending this region to the middle 
portion of the west coast of Florida. However, the storms affecting the west 
coast of Florida tend to be weaker (see fig. 8). Since the frequency of 
landf ailing storms on the west coast of Florida is low, we felt that the 
statistical techniques were not able to discriminate this difference. We 
selected milepost 1050 as the dividing point between the two regions. Again, the 
coastal orientation changes most rapidly near this point. 

3.3.3.2 Florida Coast. The Gulf and Atlantic coasts of the United States were 
considered separately because of their differences in geographical and 
meteorological conditions. Division of the Florida peninsula involves 
consideration of a number of factors, some of which suggest contradictory 
groupings. The statistical analyses as well as meteorological considerations 
(e.g., Kuo 1959) demonstrate that hurricane characteristics vary noticeably with 
latitude. This is due to both latitudinal variations in atmospheric circulation 
patterns and generally decreasing sea-surface temperature with increasing 
latitude. Warm water has been identified as an important factor in supporting 
the energy transformations necessary to maintain a hurricane circulation. These 
facts suggest that the data for all of Florida be considered homogeneous. In 
fact, the results of the cluster analysis support such a grouping for the 
southern portion of the peninsula. However, coastal orientation suggests 
dividing the data sample near the southern tip of Florida. Tropical circulation 
typically is associated with easterly flow. Therefore, storms moving from the 
east would strike the east coast of Florida. The synoptic scale meteorological 
patterns under such flows are most conducive to development and maintenance of 
hurricanes. On this basis, we suggest that there is the potential for strong 
hurricanes to affect the east coast of Florida. 

For a hurricane to strike the west coast of Florida, it must have a westerly 
component in the direction from which it approaches the coast. Usually such 
motion is associated with storms that have undergone recurvature. Recurvature, 
as opposed to more random variations in storm direction, is almost always 
associated with the tropical cyclone becoming embedded in the westerlies. This 
is usually a critical transition in the hurricane's lifecycle. When this 
happens, the upper-level outflow necessary to maintain the warm-core circulation 
is impeded. Such storms tend to weaken and some take on extratropical 
characteristics. Occasionally, hurricanes that formed in the Gulf of Mexico 
moved across the Florida peninsula in a west to east direction before recurving 
northeastward. Though intense hurricanes were reported to have struck near Cedar 
Key and Tampa Bay in the mid-1800' s (Ludlum 1963), it is reasonable to expect 
that, on the average, hurricanes striking the west coast of Florida will probably 
be weaker. The data (since 1900) in Figure 8 lends support to this observation. 



42 



3.3.3.3 Atlantic coast. When five clusters were used, the cluster analysis 
suggested that the Atlantic coast include 3 regions: (1) the southern half of 
Florida peninsula, including the west coast, (2 ) a segment from about Vero Beach 
(milepost 1600) to the vicinity of Cape Hatteras (milepost 2250), and (3) a 
region including all the coast north of Cape Hatteras. Our a priori judgment 
suggested four segments, with only the boundary in the vicinity of Cape Hatteras 
being common with the cluster analysis. The reasons for selecting milepost 1415 
at the tip of Florida have been discussed in the previous section. As mentioned 
in Section 3 .3 .2 .2 , the boundaries of a cluster represents a region, rather than 
a clearly defined point. Examination of Figure 2 7 shows that from 
mileposts 1600-1800 there is a broad minimum in frequency of landfalling 
storms. In fact, it is probably reasonable to place the boundary between 
clusters any place within this region. For this reason, we chose to maintain 
milepost 1800 as the divider between the homogeneous cluster of storms striking 
the east coast of Florida and those affecting the coast to the north. This point 
is near the Florida-Georgia state line where the coastal orientation changes from 
NNW-SSE to NE-SW. 

Both our judgment and the statistical analysis support considering the region 
from Florida-Georgia state line to the vicinity of Cape Hatteras as 
homogeneous. Conditions to the north of Cape Hatteras may not be homogeneous, 
either meteorologically or statistically. However, the region north of 
milepost 2300 is specified as "homogeneous" because of the very limited number of 
observations of landfalling storms in this area. In general, we did not base our 
analysis for this portion of the coast on the results of formal statistical 
techniques. We believed that the only way to treat this area was by exercising 
meteorological judgment. Our analysis ensured consistency and a smooth 
transition from the more data-rich areas to the south of this area. 

3.4 Interrelations Between Hurricane Parameters 

3.4.1 Brief Review of Previous Studies 

Previous studies have suggested that some interrelations between hurricane 
parameters may exist. TR 15 suggested specifically that: 

1. hurricanes with P below 92 mb have small R; 

2. for P q from 92 to 970 mb, there is "no detectable interrelation" 

between P and R when the entire Atlantic coast was considered; 
o 

3. "if the latitudinal trend [along the Atlantic coast] is removed from P 
and R, little local interrelation between P and R remains"; and 

4. hurricanes that have recurved and move toward the north-northeast tend 
to be faster (larger T) than those that are at the same latitude and 
have a more westward component in the forward velocity. 

National Academy of Sciences (1983) evaluated the FEMA storm-surge model and 
indicated that: 

1. The Tetra Tech report claimed no strong linear relations among any 
hurricane parameters were found for the Gulf region as a whole; 



43 



Table 12. — Breakpoint values for contingency tables 

Region: GLF A (0 <_ m < 4 50) GLF B (450 <_ m <1050) 

Parameter Breakpoint Breakpoint 

P Q 951 mb 965.5 mb 

R 18 nmi 2 0.5 nmi 

T 11 kn 13 kn 



2. Earle indicated tbat there was no significant relation between 
forward speed and central pressure depression over or near southwest 
Florida (see p. Ill, National Academy of Sciences 1983). This implies 
no significant relation between T and P because central 
pressuredepression is defined as the difference between P Q and a 
peripheral pressure that is usually near 1013 mb. 

3. For the middle section of western Florida coast, R and 9 seem to be 
dependent upon central pressure depression (implying dependence on 

V- 

Among suggestions listed above, Tetra Tech's claim was based on factor analysis 
applied to all storm parameters. Others were based mostly upon qualitative 
reasoning and no rigorous statistical tests were used to support the hypotheses. 

3.4.2 Methods for Testing the Interrelations Between Hurricane Parameters 

Two methods were used to examine the question of statistical independence: 
contingency tables with a Chi-square test and the Spearman test. The contingency 
table test is a categorical test while the Spearman test is a rank test. Both 
methods are described in more detail in Appendix B. 

3.4.2.1 Contingency Table with Chi-Square Test. Since the contingency table 
analysis was designed for categorical data, the hurricane parameters had to be 
separated into categories. Because the hurricane data are continuous, the choice 
of boundaries between categories was somewhat arbitrary. The separation of the 
data also had to meet the requirement that the expected count in each cell 
could not be less than five in more than 2 percent of the cells in the 
contingency table. Because of the limited sample sizes, we only used two-by-two 
contingency tables. Only two segments had enough data to allow the Chi-square 
test to be performed: the two western-most segments along the Gulf coast (GLF A 
and GLF B). The breakpoints selected to create the categories are given in 
Table 12. These breakpoint values divide the parameters into two groups - values 
of the parameter less than the given value and those equal to or above the 
breakpoint value. 

3.4.2.2 Spearman Test. The Spearman test is based on interrelations between the 
ranking (from one extreme to the other) of the observed values instead of on the 
observed values themselves. This test does not require assumptions about the 
distribution of the data; it is a non-parametric test. The Spearman test 
statistic can be computed for a sample size as small as four (Conover 1971). It 
can be used to test independence, positive correlation or negative correlation 
between ranks of two random variables. The minimum sample size that is required 
for reliable inference based on this test has not been established. Thus, the 
test results obtained for small samples must be interpreted with caution. In the 

44 



Table 13. — Sample sizes of paired parameters of landf ailing hurricanes for 
coastal segments 





GLF A 


GLF B 


GLF C 


ATL A 


ATL B 


ALT C 


Milepost 














Range 


0-4 50 


450-1050 


1050-1415 


1415-1800 


1800-2300 


2300-3 100 


(P , R) 
P , T) 

(R, T) 


23 


28 


13 


17 


16 


6 


24 


29 


13 


17 


16 


7 


23 


28 


13 


17 


16 


6 



discussion of test results, we also present the sample sizes to provide a 
qualitative indication of the reliability of test results, i.e., the larger the 
sample size the more reliable the result is likely to be. 

3.4.3 Comparison of Results from Different Independence Tests 

The comparison between results of the Spearman test and those of the 
contingency table with a Chi-square test are shown in Figure 9. In each block, 
the upper triangle shows the results of the Spearman test and the lower triangle 
shows those of the contingency table with a Chi-square test. A symbol is given 
for each intersection of a column of one parameter and a row of a different 
parameter. The symbol I means that the pair of parameters are mutually 
independent and the symbol * indicates that the sample size for the pair of 
parameters was too small for the contingency table with a "Chi-square test. 

The sample sizes of paired parameters of landf ailing hurricanes are listed in 
Table 13. For coastal segment ATL C, there were only seven landf ailing 
hurricanes recorded, and for one hurricane the R value was not available. The 
sample size for ATL C was considered so small that no formal statistical testing 
was done for this coastal segment. Only segments with sample sizes greater than 
2 were sufficient to apply the Chi-square test. 

Figure 9, indicates that each pair of parameters for the combinations of P , R 
and T are mutually independent. For the pairs that have large enough sample 
sizes, the results from the Spearman test and the Chi-square test agree with each 
other. 

3.5 Discussion 

In general, the parameters P R and T for landfalling hurricanes are mutually 
independent for the coastal segments throughout the milepost range 0-2300. For 
mileposts greater than 2300 (north of Chesapeake Bay), the small sample size 
prevents the determination of meaningful statistical results. The direction of 
storm motion is limited by the coastal orientation and cannot be treated as a 
random variable. For the purposes of storm-surge frequency computations, it is 
our recommendation, based on the results of the statistical tests and on our 
meteorological judgment, that all parameters be considered locally independent 
for the entire Gulf and Atlantic coast, except for the special cases discussed in 
Chapters 4 and 5. 

The data available for tropical storms, and bypassing and exiting hurricanes 
were inadequate to allow a statistical treatment. For landfalling tropical 
storms, only forward direction and speed were available. For bypassing and 

45 



GLF A (0 < m < 450) 





P o 


R 


T 


P o 




T 


I 


R 


I 




I 


T 


I 


I 


\ 



CHI-SQUARE 



GLF B ( 


450 < 


m < 


1050) 




p o 


R 


T 


P o 


\ 


I 


I 


R 


I 




I 


T 


I 


I 


\ 



ATL B (1800 < in < 2300) 



P R T 

P o \^ i i 

R * \^ I 

T * ■ * \ 



CHI-SQUARE 



CHI-SQUARE 



GLF C (1050 < m < 1415) 



ATL A (1415 < m < 1800) 



P o R T 

P o \ Z 1 

\ 

R * N. I 

T * * \ 





P o 


R 


T 


P o 




I 


I 


R 


* 


\ 


I 


T 


* 


* 


\ 



IHI-SQUARE 



CHI-SQUARE 



Tigure 9. — Interralatioas between parameters of landf ailing hurricanes for the 
Gulf and Atlantic coasts of the United States. Symbol m denotes milepost, I 
means independent, and * means insufficient data. 



exiting hurricanes, except for limited coastal segments, the sample sizes were 
too small for meaningful statistical tests. In practical applications, these 
classes of storms are treated as individual entities with separate frequency 
counts and different probability distributions for corresponding parameters, if 
warranted. The question of their interdependency was not resolved in this study, 
but, based on the results for landfalling storms, we feel it is reasonable to 
assume that these parameters can also be considered independent. 

While consideration of the statistical analysis was integral to our 
conclusions, our recommendations rely heavily on our meteorological judgment. 
This situation arose because the data sample was characterized by large natural 
variability. While the sampling period is on the order of a century, there are 
generally fewer than 10-15 storms per year that reach an intensity sufficient to 
be classified as tropical cyclones. In general, this amount of data is not 
sufficient to counteract the natural variability of the sample, and to allow 
standard statistical procedures to provide reliable guidance in answering the 
question of whether the parameters are mutually independent. 

We want to emphasize that our conclusion that the data can, in general, be 
considered independent should be interpreted narrowly. We feel that, given the 
data sample, there is no evidence to support quantifiable interrelations. 
Because of the variation along the coast, both in the Gulf as discussed in 
Section 3.3.2.1, and along the Atlantic coast due to the "latitude effect," 
independence should be considered to be applicable locally. This concept is 
analogous to the idea of local homogeneity, discussed in Section 3.3.2.1. For 
example, Figure 10 shows scatter diagrams of P , R, 9, and T as a function of 
milepost for the Atlantic coast. There is a fairly clear tendency for all four 
parameters to increase with the milepost value - this is the "latitude effect." 
This correlation of all parameters with latitude could lead to the conclusion, 
based on any number of statistical tests, that the parameters are interrelated. 
However, this interrelation would not necessarily be between the parameters 
themselves, but could be due to the latitude effect. For any limited area, even 
if sufficient data were available, we feel that it is likely that the parameters 
would be mutually independent. Because we present our results (chapts. 6-9) with 
respect to milepost, the latitude effect, while being incorporated into the 
analysis, has effectively been removed for the purposes of local storm-surge 
computations. 

Our recommendation that the parameters be treated as locally independent is not 
meant to imply that we feel there are no interrelations between the 
four parameters. Meteorologically, there are good reasons to suspect such 
relations. What we are proposing is that the natural variability in the data 
sample completely overwhelms any interrelations that may exist. The 
recommendation is a practical one - there is no way, within the limits of this 
study, to quantify interrelations between the parameters. Except for the special 
cases discussed in Chapters 4 and 5, there is no justification for attempting to 
specify, rather arbitrarily, possible interrelations. Further analysis of data 
from areas beyond those considered in this study may be sufficient to determine 
whether interrelations do exist, and to support quantification of such 
relations. However, if such work were to be pursued, care should be taken to 
assure that conclusions drawn from such a study were applicable to storm-surge 
computations along the Gulf and Atlantic coasts. 



47 



»oo 139* i*oo iToo iao» noo iooo 210* 2200 2Jo« 2«as 23ot !tti 2Tot :«o. 2*1* sot* not Ugi 



MILEPOST (ami) 
(a) Central Pressure 



no ISO! !*«• -700 



2000 2100 2200 2300 2100 2300 2M0 2700 



2900 300* 310* MOO 



MILEPOST (nmi) 
(b) Radius of maximum winds 



Figure lO.-Landfalling hurricane parameters versus adlepost for the Atlantic 

48 



coast. 



i»9< 1:39 itci 1T0* :ano i«o» 2oao 2109 2209 2399 2*09 23a* 2* 

MILEPOST (nmi) 
(c) Forward direction 



2ioa loo* ;iai 



1»10 1509 1*00 1730 1300 1909 



U00 220* 230* 2»aO 2S09 2*00 2T09 

MILEPOST (nmi) 
(d) Forward speed 



2191 3009 3109 3209 



Figure 10. — (continued). 



49 



4. THE JOINT PROBABILITY QUESTION: 
CENTRAL PRESSURE VERSUS RADIUS OF MAXIMUM WINDS 

4.1 Introduction 

An objective of this report "was to define climatological probability distribu- 
tions of hurricane central pressure (P Q )> radius of maximum winds (R) , forward 
speed (T), and direction of motion (9) along the Atlantic and Gulf coasts. In 
calculating frequency distributions of hurricane-induced surges on the coast it 
is necessary to combine the probabilities from the individual distributions. In 
such applications, the question of statistical independence among the individual 
probability distributions has to be addressed. For example, of all the hurri- 
canes affecting a given coastal stretch over a long period of time, what fraction 
of the storms are in both the upper 10 percent in intensity (P ) and size (R)? 
If P and R are independent, the probabilities can be multiplied. In this case, 
there would be a 1-percent chance of their joint occurrence. If P and R are 
positively correlated, there would be more than a 1-percent chance of the simul- 
taneous occurrence of a storm both this intense and this large. Similarly, if P 
and R are negatively correlated, the joint probability is less than 1 percent. 

Statistical tests may be inappropriately biased toward acceptance of indepen- 
dence if the significance level chosen for the test is too low, especially 
considering the high variability and relatively small sample sizes available for 
this study. Dependencies which are meteorologically based may be present, but 
may not lead to rejection of the null hypothesis of independence. Another point 
that must be considered is whether or not certain interdependencies are expected 
to extend across the entire spectrum of a given parameter or whether such 
relations might be important only within some limited range of values. 

4.2 Central Pressure Versus Radius of Maximum Winds 

A significant joint probability question is whether hurricane size (R) and 
intensity (P ) are independent. A storm that is both large and intense would 
have enormous destructive power. Hurricanes with very large R's (in excess of 
4 5 nmi) are generally found to be of moderate or weak intensity. In hurricanes 
that have undergone recurvature and are moving northward in the Atlantic, often 
becoming ext ratropical , the radius of maximum winds tends to become larger and 
more ill-defined, and the central pressure rises. Extremely intense hurricanes 
(low P ) and those with small radii of maximum winds tend to occur together 
because, if angular momentum is conserved, a vortex contracts in size as it 
increases its rotational speed. 

If we examine the data for P and R for the Gulf coast (table 1), it is not 
surprising that the calculated correlation coefficient was only 0.16. A 
correlation coefficient this low indicates that the linear relation between P q 
and R is not likely to be significant. However, a low correlation could occur if 
a nonlinear relation existed between these two variables. It is also possible 
that a relation between P Q and R could be masked by the high degree of natural 
variability inherent in hurricane observations. If such a relation exists, it is 
likely to be most prominent for intense storms where the dynamics that couple the 
variation of both P and R are stongest and less susceptible to the masking 



dependence of P and R, we choose to employ non-parametric statistics. A 



non- 



parametric test does not require specification of the form of the distribution, 



50 



Table 14. — An example of a general two— by— two contingency table 



Condition 1 Condition 2 Total 



Group 1 a b a + b 

Group 2 c d c + d 

Total a + c b + d n 



thus, Che statistical test avoids the assumption of linearity. It can also 
provide insight into behavior of the extreme portion of the distribution by 
judicious selection of the P Q and R groupings. (See below.) 

The test of interdependence of P Q and R involves comparing the two samples of 
observations to see if the populations appear co be related. In other words, to 
determine if a given P Q value is more likely to be associated with a limited 
range of R values (interdependence), or whether any R from the complete spectrum 
of values has the same probability as the distribution specified for R for every 
? value (independence). We set up a contingency table, the form of the 
tabulation is displayed conventionally in Table 14. The letters a, b, c, and d 
3 re the count of occurrences in each group for a given condition. 

We used Fisher's exact probability test (Conover 1971) to compare our 
groupings. Fisher's test assumes that the marginal totals of Table 14 are fixed 
(that is, the number of observations in each group and for each condition are 
fixed), and tests whether the partitioning of frequencies (a, b, c, d) could have 
arisen by chance. The probability of such an occurrence is calculated as, 



a + c 



( b ; d ) 



n 
a + b 



where ! "' '" j is a binominal coefficient ; — ; — - , hence 



= (a + b)! (c + d)! (a + c)! (b + d) 
P ~~ n! a! b! c! d! 



51 



Table 15. — Frequency of occurrence of different storm radii in two different 
class intervals of hurricane intensity observed in the Gulf of Mexico, 1900-84 

R < 15 nmi R > 15 nmi Total 



P Q > 93 mb 16 47 63 

P Q <_ 93 mb 3 3 

Total 19 Ul 66 



Table 15 sbows tbe number of occurrences of burricanes making landfall on the 
Gulf coast, within different categories of central pressure and storm size. We 
formed a null hypothesis, H Q , that there was no significant difference between R 
associated with group 1 (P Q > 930 mb) and group 2 ( P Q < 93 mb). Fisher's test 
gives a probability of occurrence by chance a value of 0.02. At the 5-percent 
level we rejected H and concluded that there was a significant difference 
between the two groups of hurricanes, in terms of occurrence of the specified 
hurricane radius. 

A similar test was applied to the parameters, P Q and R, for hurricanes 
landfalling on the Atlantic coast. With a small sample size and a much larger 
degree of scatter, the formal statistical test could not detect any significant 
interdependence of these two parameters for Atlantic coast hurricanes. While it 
is clear that a relation appears to be reasonable for the extremely intense 
hurricanes, natural variability seems to overwhelm this effect for most of the 
other (weaker) storms. Furthermore, it requires a much larger sample of data to 
establish the functional form of the joint probability of two parameters with a 
degree of reliability, as compared to specifying a single probabilitv 
distribution. 

The hurricanes listed in Tables 1 and 2 are insufficient to auantify anv joint 
probabilitv relation that might exist over the full range of P and R. The data 
must be supplemented by a measure of deduction and meteorological judgment. 
Before reaching a conclusion, we supplemented our data base by including 
extremelv intense hurricanes that occurred outside our main area of interest 
(within 150 nmi of the Gulf and Atlantic coasts). 



4.3 Meteorological Analysis 

The basic observations used in our analysis of extremely intense hurricanes 
(P<93 mb) were based primarily on wind and pressure data recorded by recon- 
naissance aircraft. In some cases, central pressures were also obtained from a 
search of other sources, including studies of individual hurricanes in the liter- 
ature. Table 16 gives a list of hurricanes with P Q less than or equal to 93 mb 
recorded during the period 1900-85, together with the radius of maximum winds 
taken at the time of minimum central pressure. The R values for Hurricane Janet 
of 1955 could not be determined because of a lack of wind data. Janet was a very 
compact storm with winds reaching hurricane force only about 2 hr before the 
arrival of the eye (Dunn et al. 1955). Estimated maximum winds of 2 00 mph were 
reported just about 30 min prior to the passage of the eye over Swan Island. The 
table also lists locations where the P and R data were observed. In all cases, 

52 



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53 



the central pressure (P Q ) given in Table 16 is the lowest pressure observed in 
the entire life span of each hurricane. The notation P Q used to designate the 
central pressures in Tables 1 through 3 carries a different connotation. Tables 
1 through 3 list the pressure that would generate a realistic surge on the open 
coast in steady-state models currently used in flood insurance studies (relative 
to the coast). In this chapter, P is used to signify the central pressure 
values without reference to the time or place of observation (absolute minimum 

V- 

Figure 11 shows the locations of the 15 extreme hurricanes at the time of their 
lowest central pressure. Out of the 15 extreme hurricanes, 6 occurred in the 
Atlantic Ocean. The hurricane of 193 5 which struck the Florida Keys had the 
lowest central pressure ever recorded in Atlantic hurricanes (892.5 mb). The 
most intense hurricanes affecting the Gulf coast were Hurricanes Camille (1969) 
and Allen (1980). A record low central pressure for the Gulf of Mexico (899 mb) 
was reported in Hurricane Allen as it entered the Gulf of Mexico through the 
Yucatan Channel. 

Figures 12 and 13 show the tracks of these severe hurricanes together with 
locations of reported lowest pressures at various times during the life span of 
each hurricane. Central pressures of 905, 908, and 909 mb were observed in 
Hurricane Camille (1969) near 2 5°N, 28°N, and at the time of landfall. There was 
insufficient data to show detailed time variation of Camille's intensity between 
the time she crossed 2 5°N and the coast. We assumed that Camille's central 
pressure remained almost steady during this time period of about 3 6 hours. 
Hurricane David (1979) reached its minimum pressure of 92 4 mb when the hurricane 
was located some 100 nmi south-southeast of Puerto Rico. Its central pressure 
rose above 93 mb and then dropped to 92 6 mb just before crossing the coast of 
Hispaniola. Low pressures in Hurricane Allen (1980) were plotted at three 
different locations because Allen went through three weakening/deepening cycles 
in its life span. The occurrence of these three cycles in Allen strongly 
suggests that geographical location is not a limiting factor in the occurrence of 
extreme hurricanes. 

4.4 Discussion of Analysis 

Figure 14 shows a plot of P versus R for the hurricanes listed in Table 16. 
Data from Hurricane Carla (1961) and a few data points from Allen (1980) (when P Q 
was slightly higher than the minimum of 899 mb) were plotted in the same figure 
to aid in determining the envelope of possible R values for extreme hurricane 
conditions. An envelope was drawn through the highest R values for selected 
intervals of central pressures. This curve indicates that observations of 
extremely intense hurricanes with P less than 92 mb consistently have small R 
values. The question of possible interdependence of P and R appears to be 
clearest for the most intense hurricanes. 

The second question which follows is whether the group of hurricanes included 
in Figure 14 are representative of landfalling hurricanes. Of the six Atlantic 
hurricanes, the 'Labor Day' hurricane (193 5) which had the lowest central 
pressure ever recorded in the Atlantic, struck the Florida Keys. Hurricane 
Camille reached its maximum intensity in the Gulf of Mexico; its central pressure 
appears to have remained almost steady for the 36 hours before it crossed the 
coast. Hurricanes David, Inez, Hattie, Carmen, Janet and Anita (see fig. 11) 



54 



«» 






O 

o 



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a 




Sjs^v 



55 




56 




57 



930 



920- 






910 



900 



89Q 



• O 
X 



X • 




/ 




ATLANTIC HURRICANE 

CARIBBEAN " • 

GULF " X 

ALLEN & 



5 10 15 20 25 

RADIUS OF MAXIMUM WINDS (nmi) 



30 



Figure 14. — Plot of P versus R for extreme hurricanes listed in Table 16. 
Additional data points from hurricanes Carla (1961) and Allen (1980) have been 
included* 



58 



reached their maximum intensity prior to the time of landf ailing. The weakening 
of Hurricane Allen (1980) prior to the time of landfall can he explained by the 
presence of a warm high pressure ridge over the southern states. Similarly, 
other cases of decreasing intensity prior to landfall could not be simply 
explained due to the close proximity of the land mass. There is no reason to 
believe that, under reasonable meteorological conditions, any of these hurricanes 
could not have reached the coast while maintaining their maximum intensity. 

4.5 Conclusions 

There are insufficient data to specify a joint probability distribution of P 
and R for extreme hurricanes on a regional basis. Intense hurricanes were 
experienced on the Gulf coast, extending from the Florida Keys (1935 hurricane) 
through the Mississippi coast (Camille 1969) to locations off the Texas coast 
(Hurricanes Allen, Anita and Beulah). Small R's tended to be associated with 
these hurricanes when their pressures were lowest. These facts suggest that 
small R's are associated with intense hurricanes. There are seven observed R 
values for hurricanes with central pressure less than 92 mb. These R values, 
ranging from 6 nmi to 15 nmi, have both mean and ^median values of 10 nmi. It 
appears that 10 nmi is a representative R value" for intense hurricanes. A 
refinement can be accomplished by separating the intensity of the storms into two 
different class intervals. We believe that an R value of 13 nmi assigned to the 
class interval of 92 0-908 mb and an R value of 9 nmi assigned to storms with P 
less than 908 mb would provide reasonable estimates consistent with observations 
and accepted meteorological principles. We recommend the adoption of these 
R values for the most intense hurricane categories. 



5. OTHER JOINT PROBABILITY QUESTIONS 

5.1 Introduction 

Unlike P , R and T, 9 is restricted to ranges that depend on coastal 
orientation, and, as discussed in Section 3.2.1.2, creates problems in treating 
the direction data as a random sample. This chapter will attempt to examine 
possible interrelations between P and 0, and between T and 9. While we will use 
some formal statistical procedures, we want to emphasize that it is only for the 
purpose of guiding our judgment about possible interrelations. Ho and 
Tracey (1975) discussed in some detail possible relations between P and 6. It 
appears that this interrelation is a localized problem for North Carolina, north 
of Cape Hatteras. With the limited number of observations, it is not feasible to 
specify the joint probability of the two parameters. To establish such a joint 
probability relation requires a much larger sample size than that required for a 
single probability distribution. An alternative approach in dealing with this 
problem is to segregate the sample into subgroups. 



* 

It should be emphasized that the representative R value is a clima tologi cal mean 
which excludes probable extreme values and may not be applicable in engineering 
design and forecasting. 



59 



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DIRECTION (deq. from north) 

Figure 15. — Scatter diagram of direction versus speed of forward notion for 
hurricanes landfalling on the Atlantic coast. 

5.2 Forward Speed versus Direction of Storm Motion 

In Che Atlantic, hurricanes tend to move north-northeastward to northeastward 
after they recurve. These hurricanes generally move faster than westward moving 
hurricanes at the same latitudes. Atlantic hurricanes that recurve near the 
coast often strike either the North Carolina coast or the south shore of Long 
Island or New England. Figure 15 shows a scatter diagram of direction versus 
speed of forward motion for hurricanes landfalling on the Atlantic coast. This 
figure reveals that a direction of about 180° appears to separate the speeds into 
two groups. The group with high speeds (right hand side of fig. 15) is 
associated with directions from 180-220°, while the slower speeds are associated 
with the full range of directions. This suggests that landfalling hurricanes 
moving north-northeastward tend to have higher speeds of translation than those 
coming from a direction with an easterly component. It is of interest to note 
that these fast-moving storms entered the coast north of 33.5°N. These 

hurricanes crossed the coast either near Cape Hatteras, North Carolina or in the 
Long Island-New England area. These are the only areas along the Atlantic coast 
whose coastal orientation allows storms moving from this general direction to be 
classified as landfalling hurricanes. Storms entering the coast south of Cape 
Hatteras, North Carolina, are generally hurricanes of Atlantic origin that move 
in a northerly direction after recurvature or those that exited the Florida and 
Georgia coast. Storms landfalling on the south shore of Long Island or New 
England are usually hurricanes that moved parallel to the coast of Maryland, 
Delaware and New Jersey. They could be classified as alongshore storms for 
coastal locations to the south of the point where they made landfall. There are 
no landfalling hurricanes coming from the directions 180-220° south of 33.5°N 
because of the way storms are classified: by definition, storms coming from those 
directions (180-220°) are either exiting or alongshore storms. 



60 



Table 17. — Comparison of speeds of landf ailing and alongshore storms for the 
vicinity of Charleston, South Carolina 

Percent of storms 5 20 40 60 80 9T 



Landf ailing storms (kn) 5.6 7.2 9.5 12.2 15.1 19.2 

Alongshore storms (kn) 6.6 8.6 10.8 13.5 17.6 23.5 

Difference TTo l74 K3 HI FT! 4~7T 



As indicated in Chapter 3, 9 and T for landf ailing storms generally vary with 
increasing latitudes. The correlation coefficient of T and landfalling latitude 
on the Atlantic coast is 0.71, and 0.45 for 9 and latitude. An examination of 
the scatter diagram for T versus latitude (see fig. lOd) reveals that hurricanes 
with speeds greater than 20 kn struck the coast north of 33°N, and that all the 
hurricanes which crossed the Long Island-New England coast were fast-moving 
storms. Thus, hurricanes landfalling at the northern latitudes tend to move at 
higher speeds than those making landfall to the south. Though there are 
limitations in the data samples for 9 and T as previously indicated, it appears 
that hurricanes landfalling on the northern Atlantic coast may be different from 
those making landfall to the south. However, when we examined the data within 
homogeneous regions (concept of local homogeneity, as discussed in sec. 3.3.2.1), 
9 and T for landfalling hurricanes appeared to be independent. The apparent 
relation is attributed to the latitude effect, as discussed in Section 3.5. 

Figure 16 (from Myers 1975) shows cumulative probability curves of forward 
speed for alongshore and landfalling storms for the Charleston, South Carolina 
area. The plots suggest that alongshore storms move only slightly faster than 
landfalling storms. Twenty percent of alongshore storms move at speeds faster 
than 17.5 kn, while 20 percent of landfalling storms move at speeds faster than 
15 kn. Differences for the other 80 percent of storms are typically just over 
1 kn, as shown in Table 17. This difference is within the range of expected 
error in measuring storm speeds and suggests no relation between T and 9. 

5.3 Central Pressure versus Direction of Storm Motion 

5.3.1 Gulf Coast 

Hurricanes landfalling on the Gulf coast generally arrive at the Texas coast 
from an easterly direction, or strike the Florida Panhandle, Alabama, Mississippi 
and Louisiana coasts from a southerly direction or cross the west coast of 
Florida from the south-southwest to the southwesterly directions, as shown in 
Figure 17. It would be easy to assume that these track directions come from 
different populations. The Mann-Whitney test, which can be used to evaluate the 
homogeneity of two samples, indicates that there are significant differences 
among track directions in the three different zones on the Gulf coast. However, 
the solid line in Figure 17 is the variation of the perpendicular drawn to the 
smoothed coastline of Figure 1. The close correspondence between the data and 
this line is simply a result of the restriction in directions imposed by 
classifying these storms as landfalling hurricanes. Tests of interdependence of 
P and 9 using contingency tables and the Spearman rank tests for the three zones 

61 



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r CRWARD SPEED (kn) 



Figure 16. — Probability distribution of forward speed of (a) landf ailing, and 
(b) alongshore hurricanes in the vicinity of Charleston, South Carolina, for 
the period 1386-1973 (from Myers 1975). 



62 




530 400 600 300 1000 1200 1400 1600 

MILtPOST Cnmi) 
Figure 17. — Plot of forward direction versus ailepost for the landf ailing 
hurricanes on the Gulf coast of the United States. The solid line is the 
perpendicular to Che coastal orientation as a function of siilepost value. 



50 



45-- 

2 40:- 

a 

- 35:- 



o 

t 30i 



25 : 



20- r 



20 



40 



80 100 120 140 160 
FORWARD DIRECTION (dag) 



80 



200 220 



Figure 18. — Variation with latitude of direction of forward motion for hurricanes 
landf ailing on the Atlantic coast. 



63 



Table 18. — Partition of P Q and 9 for landfalling hurricanes striking the Atlantic 
coast south of 33.5°N 



P o i. 945 mb p > 945 mb Total 

9 >_ 95° 3 15 18 

9 < 95° 4 4 

Total 3 19 22 



separately show no evidence of interrelations between the parameters. However, 
this conclusion must be interpreted narrowly: independence is with respect to 
landfalling storms. Because of the variation of the coastline, this should also 
be considered locally independent, in the same sense as described in 
Section 3.5. It should not be extended to the underlying populations that 
contain the full range of possible values without more detailed and extensive 
analysis. 

5.3.2 Atlantic Coast 

On the Atlantic coast, the interrelations of P Q and 9 are masked by their 
correlations with latitude. Figure 18 shows the variation with latitude of the 
direction of motion for hurricanes landfalling on the Atlantic coast. The plot 
suggests two groups of storm track directions. These two groups appear to be 
separated by a forward direction of about 170° (vertical line on fig. 18). From 
a meteorological standpoint, the data sample suggests the existence of two 
distinct groups: (1) landfalling hurricanes crossing the Atlantic coast from 
easterly directions (20-170°), which are westward moving hurricanes embedded in 
the basic easterly current, and (2) landfalling hurricanes coming from 170-220°, 
which are hurricanes moving northeastward after recurvature. There is also a 
stretch of the coast, from 33.5-3 7°N, which apparently includes hurricanes from 
both groups (dashed horizontal lines in fig. 18). 

Statistical tests of homogeneity, using contingency tables and the Mann-Whitney 
test, indicate that storm track data north of 37°N are significantly different 
from similar data Co the south. These results also suggest that there are two 
distinct groups of storm-track directions for landfalling hurricanes along the 
Atlantic coast. Since the data along the entire Atlantic coast cannot be 
considered homogeneous, it is inappropriate to consider the interdependence of P 
and 9 for these data without separating the sample into separate groups. 

5.3.2.1 Atlantic Coast, South of 33.5°N. We considered the data sample of 
landfalling hurricanes for the Atlantic coast, south of 33.5°N, in the form of a 
2X2 contingency table. We estimated the probability that specific 
partitionings of the frequencies arose by chance. One partition of the data can 
be made as shown in Table 18. This contingency table shows the number of 
occurrences (frequencies) of hurricanes within different categories of P Q and 
9. We then formed a null hypothesis that the noted distribution of observations 
(frequencies) arose by chance, that is, there was no significant difference 
between 9 _> 95° and 9 < 95°. The Fisher exact probability test gives a 0.53 
probability of occurrence by chance. This indicates that we cannot reject the 
null hypothesis at the 5-percent level. We further tested for different 
groupings by changing the dividing line for both track directions and central 
pressures. These tests also yielded results which did not allow us to reject the 

64 




145 £30 215 200 185 170 155 140 
DIRECTION (deg) 



10 95 



Figure 19. — Histogram for direction of storm motion for the 2.5' 
longitude block centered about Key West, Florida. 



latitude and 



null hypothesis. We concluded that, at the 5-percent level, there is no 

significant difference between the two groups of hurricanes, in terras of 

occurrence of the specified direction of storm motion. In other words, there is 

no detectable relation between P and 9. 

o 

This conclusion is based on the total data sample. However, there may be 
localized areas that could exhibit characteristics different from this general 
conclusion. The data sample is inadequate to detect such situations. For 
instance, an interrelation between P and might occur locally near the southern 
tip of the Florida peninsula and the Florida Keys. Figure 19 shows a histogram 
for direction of storm motion for a 2.5 degrees latitude and longitude block 
centered about Key West. This histogram indicates a bimodal distribution for 
direction of storm motion with storms traversing the 2.5 degree block both from 
the southeast and the southwest. It is generally observed that storms coming 
from an easterly direction are more intense than those coming from a westerly 
direction. These localized interrelations between P , 9, and possibly between 
other parameters need further scrutiny. It is left to the user of this report to 
look at conditions at specific locations more closely. The treatment of storms 
affecting the Cape Hatteras area that follows in Section 5.4 may be used as a 
guide. 



65 



5.3.2.2 North Atlantic Coast. Examination of Figure 10a showing the latitudinal 
variation of pressure suggests no noticeable variation with milepost for the 
northern Atlantic coast. Meteorological conditions associated with the increase 
in central pressure with increasing latitude are discussed in Chapter 7. This 
feature is not obvious from Figure 10a. Consideration of Figure 10c for storm 
direction shows a variation due in part to variations in coastal orientation, but 
primarily due to synoptic-scale meteorological conditions. A large scale high 
pressure system (the Azores-Bermuda high) usually is centered off the coast 
creating a clockwise flow around it during the hurricane season. In association 
with this high pressure system, storm direction tends to turn clockwise as the 
storms move northward. This is the main explanation for the variation shown in 
Figure 10c. In the absence of adequate data to test for interrelations 
independent of latitude, it is our judgment that the concept of local 
independence is appropriate for the northern part of the Atlantic coast. 

5.4 Cape Hatteras Area 

There are a number of coastal locations that, because of geographical features, 
are probably not well represented by the generalized results presented in this 
report. Such areas include protrusions, such as the Mississippi delta, the 
southern part of Florida, Cape Hatteras and Cape Cod. It also includes major 
bays and partially enclosed bodies of water, such as Chesapeake Bay, Delaware Bay 
and the New York Bight. The paucity of storms affecting any one of these areas 
makes generalized analysis such as done in this report impossible. They must be 
examined on an individual basis. To illustrate some factors that might be 
considered in such an analysis, we studied the area around Cape Hatteras. What 
follows includes consideration of the more important factors for this particular 
location. Some aspects of the approach might not be equally appropriate for 
other locations. 

One reason for selecting Cape Hatteras was based on consideration of 
Figure 18. It appears that between 33.5 to 37.0°N, the storms may include 
different types of hurricanes. For the coastal region from Cape Hatteras, North 
Carolina to Virginia Beach, Virginia on the Atlantic coast, hurricanes 
landfalling from the southeast quadrant cover the full range of intensities from 
severe to weak. Occasionally, a hurricane meanders and strikes this stretch of 
the coast from the northeast quadrant; observations indicate that these storms 
have been weaker than those coming from the southeast. They have been weakened 
either by unfavorable conditions in the troposphere or by the reduction of energy 
supply while drifting over cold water. These storms, which typically move at 
less than 15 kn, generally have slower speeds of translation than storms entering 
the coast from the southeast quadrant. Therefore, a separation of P and T, as 
well as P and Q, between landfalling storms from the southeast and northeast 
quadrant was considered. The data for all landfalling hurricanes do not suggest 
that R differs much depending on 9. Therefore, the R probability distribution as 
given in Chapter 8 is recommended for both storm categories. Portions of the 
statistical treatments used below were formulated by Ho and Tracey (1975). 

5.4.1 Parameters for Landfalling Hurricanes from Northeast Quadrant 

A special analysis was made of tropical cyclones landfalling from the northeast 
quadrant. Hurricane Doria (1967), which was a tropical storm at landfall, was 
used from Table 2, and, to expand the sample, data from other tropical cyclones 



66 



(1886 to 1984) moving from a northeasterly direction within an area west of 70°W 
and north of 32 °N were also used. Tracks for Doria and these seven additional 
storms are shown in Figure 2 0. These eight central pressure values were used in 
the estimation of the cumulative probability curve shown in Figure 2 1 
(curve A). The speeds of forward motion for the same storms were measured from 
storm track maps (Neumann et al« 1981), and were used to help establish the 
probability distribution shown in Figure 22 (curve A). 

5.4.2 Parameters for Landf ailing Hurricanes from Southeast Quadrant 

To obtain the probability distribution of central pressure for storms 
landfalling from the southeast quadrant, the probabilities for northeast quadrant 
tropical cyclones were subtracted from the overall probability for all 
landfalling storms. The probability distribution thus obtained was also checked 
against a direct sample of storm data. The resultant distribution for the 
southeast storms (fig. 2 1, curve B) differs only slightly from that of all 
landfalling storms. Speed of forward motion probabilities were evaluated in a 
similar manner (fig. 22, curve B). 

5.4.3 Landfalling Track Frequency 

A discontinuity of track directions at Cape Hatteras can be seen between the 
curves in Figures 44 and 45. The frequency of storms landfalling from the sector 
91-160° is approximately the same immediately north and south of the Cape. 
Landfalling storms from the other possible directions - 160-240° south of the 
Cape and from the northeast quadrant north of the Cape - are not of equal 
frequency. The overall frequency of landfalling storms (fig. 27), which was 
averaged along the coast by using a smoothing function, was adjusted to define 
this discontinuity. A track count of storms from the northeast quadrant and the 
91-160° sector crossing overlapping two-degree latitude and longitude squares was 
examined separately. The sum of these frequencies was checked against the 
frequencies of all landfalling tropical cyclones. Figure 23 shows the resulting 
frequencies with which hurricanes and tropical storms entered the coast from 
different sections both north and south of the Cape. The plotted points show the 
frequencies of all tropical cyclones at 50-nrai intervals (determined from 
fig. 27). 

6. FREQUENCY OF HURRICANE AND TROPICAL STORM OCCURRENCES 

6.1 Classification of Hurricanes and Data 

The frequency with which a coastal area has experienced tropical storms and 
hurricanes during the period 1871-1984 is analyzed in this chapter. The data 
have been divided into three categories of storms that affect the coast in dif- 
ferent ways: 1) landfalling storms, 2) exiting storms, and 3) alongshore 
storms. The frequency of storm occurrences is defined as the number of tracks of 
each category of storms per year per nautical mile along a smoothed coast. The 
term "smoothed coastline" is discussed further in Section 6.2.1.2 and a smoothed 
coastline, defined objectively, is shown in Figure 24. 

The statistics on the frequency of hurricane and tropical storm occurrences are 
based on the yearly storm track charts by Neumann et al. (1981) from 1871-1980, 
and from their annual updates between 1981-1984 (published in Monthly Weather 
Review ). Following the criteria used in the track charts, tropical storms are 

67 





+ 



JUL. 1934 



+ 



4- 



OCT. JUL. 
I 897 I 90 I 



SEPT. 
1889 
/ SEPT. 
1967 



SEPT. 
972 



+ 



OCT. 
913 



NOV. 

I 935 



Figure 2 0. — Track of tropical storms and hurricanes showing motion from northeast 
(from Ho and Tracey 1975). 



68 



RETURN PERIOD (yr) 



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(A), 

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CUMULATIVE PROBABILITY 



I I I I I I l I I I l I 



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Figure 21.— Cumulative probability curve of central pressure for landf ailing 
tropical cyclones adapted for Wright Monument, North Carolina. 



RETURN PERIOO (yr) 



3 4 5 

'I ' I 



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t— I — i' " i : i ' i ' i ' i i ' ; n ' ! i 



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NE LANDFALLING STORMS 
WRIGHT MONUMENT, N.C. 



i i i i i i i i i i i i 



• 1 .5 1.0 5 10 20 30 40 50 60 70 30 90 95 96 97 38 99 99.3 99.7 99.8 99.9 

CUMULATIVE PROBABILITY 

Figure 22.— Cumulative probability curve of speed of storm notion adapted for 
Wright Monument, North Carolina. 

69 



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Figure 24. — Smoothed coastline obtained by applying the objective smoothing 
function. 



71 



defined as storms with maximum winds 34 to 63 kn, and hurricanes as storms with 
winds 64 kn or greater. The track charts also show extratropical stages of the 
cyclone tracks when the tropical circulation was modified as the cyclone moved 
into a nontropical environment. Beginning in 1972, the term subtropical was 
adopted as official terminology to describe such storms. Satellite imagery and 
other observational evidence enabled Hebert and Poteat (1975) to reexamine the 
official Atlantic hurricane tracks and to identify subtropical portions of the 
cyclone tracks since 1968. We included, in our frequency counts, subtropical 
storms and extratropical storms which have intensity equal to or greater than 
that of a tropical storm. For conciseness we use the term "tropical cyclone" in 
this report to include all four classifications. Storms classified as "tropical 
depressions" and "subtropical depressions" (maximum winds less than 34 kn) are 
not included in the statistics. 

6.2 Frequency of Landfalling Tropical Cyclones 

Determination of the frequency of landfalling storms in a given area would be 
relatively simple if a sufficiently large sample were available. However, data 
are available for only 114 years, from 1871-1984. Inspection of this sample 
reveals variations within short coastal strips which are likely to be chance 
occurrences due to the relatively small sample size. A goal of this report was 
to smooth out such variations, and to portray the characteristics of the 
population , not the variability of the samples. Special effort was made to take 
into account the effect of coastal orientation on the frequency of storms. 

6.2.1 Direct-Count Method 

The most direct method of assessing the frequency of landfalling tropical 
cyclones is to count the number of storms striking the coast. The number of 
entries was totaled for each 50-nmi segment along the smoothed coastline from a 
point some 2 50 nmi south of the Texas-Mexico border to the Maine-Canada border 
(see fig. 24). We created extensions of the Gulf and Atlantic coastlines at the 
tip of Florida. We "extended" the Gulf coast from Cape Sable to the Keys, 
stopping at its intersection with 81 °W longitude, as shown in Figure 2 5. We 
"began" the Atlantic coastline at approximately 82.5°W, and continued it eastward 
along the Florida Kevs to the mainland (see fig. 2 5). A storm could only be 
counted once on each "coast." The extensions were used for estimation of the 
probability distributions of storm frequency, P and R. We did not use the 
coastal extensions for T and 9, since these data sets included both hurricanes 
and tropical storms; we felt that the data were adequate to resolve the variation 
of T and 6 along this part of the coast. The Gulf coast analysis stopped, and 
the Atlantic coast analysis began at coastal reference point 1415. 

For the period 1871-1984, 307 tropical cyclones entered the Gulf coast, and 193 
entered the Atlantic coast, not including storms passing the Florida Keys west of 
81 °W. The 50-nmi segment counts were smoothed by using the smoothing function 
described in Section 6.2.1.1. Figure 2 6 shows the frequency plot of these 
discrete storm entry values at 50-nmi intervals (points joined by a dashed line) 
and the smoothing obtained as described in the next section. These frequencies 
depict tracks of storm centers, but do not take into consideration the lateral 
extent of coast affected by an individual hurricane. The damage swath from a 
major hurricane can cover more than 100 nmi of coastline. The frequencies of 
occurrences given in terms of storms per 100 yr per 10 nmi of the coast (vertical 
scale in fig. 2 6) represent long-term averages of tropical cyclones which include 

72 






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coast through the Florida Keys. Numerals are ndlepost between 1395 and 1500 
(see fig. 1). 



73 



— EA3TPCRT. ME. 



■•-BOSTON. MASS. 



— NEW YCRK, N.Y 



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74 



storms ranging in intensity from weak tropical storms to intense hurricanes. In 
a probabilistic sense, one storm per 100 years should be interpreted as that 
event which has a 1-percent chance of occurrence per year over a 10-nmi coastal 
segment. 

6.2. 1.1. Objective Smoothing Procedure. The 50-nmi segment counts were smoothed 
by weighted averaging over 11 data points. We used a weight function in the same 
manner as in low-pass filtering in time series analysis. The adopted function 
has the following assigned weights (after Craddock 1969): 

W n = 0.300, 0.252, 0.140, 0.028, -0.040, -0.030; for 

n = 0, ±1, ±2 , ±3, ±4, ±5, respectively. 

An alternative smoothing procedure sometimes applied in climatological analyses 
uses a running-mean [W = 1/(2N+1)]. The results thus obtained may have 
distortions in phase angle variation (shifting of maximum or minimum 
positions). The weighting function adopted here is designed to maintain the 
average frequencies and phase angles of the original input series. These weights 
were applied to all successive discrete values from south of Texas to the 
southern portion of Florida, and from Key West to Maine. The end of the input 
series was extended as a mirror image of the original series. Thus, smoothed 
frequency estimates of landf ailing tropical cyclones for each 50-nmi interval 
were obtained along the smoothed coastline, from Texas all the way to the 
Canadian border. The two series were then connected to give a continuous 
smoothed curve of frequency of landfalling tropical cyclones (solid curve of 
fig. 2 6). Figure 27 shows the final frequency curve including an extension at 
the southern tip of Florida depicting the frequencies for the Florida Keys (upper 
portion of the curve). 

6.2.1.2 Evaluation of Procedure. The direct count method derives its data from 
a count of tropical cyclones at the coast and not out over the water. It gives 
the best estimate of the variation along a smooth coastline of the frequency of 
landfalling storms. However, it tends to obscure variations due to coastal 
shape. A stretch of the coast that turns sharply in a direction almost parallel 
to that of the predominant storm motion is less exposed than adjacent coastal 
segments more nearly normal to the track direction. We have implicitly smoothed 
sampling variability associated with small scale variations of the coast. 

To identify areas where the implied smooth coastal direction differs 
significantly from the actual coastline, a smoothed coastline was constructed. 
Coastal locations at 50-nmi intervals along the Gulf coast and Atlantic coast 
were smoothed using the smoothing function described in Section 6.2.1.1. These 
points were plotted and a continuous line joining these points was drawn for both 
the Gulf and Atlantic coastlines (fig. 24). This diagram reveals that this 
smooth line cuts across the actual coastline at several places — most 
significantly, across the Mississippi Delta, along the west coast of Florida and 
across Cape Cod. For the most part, the smoothed coastline approximates quite 
well the orientation of the actual coast. 

Areas where a smoothed coastal direction differs substantially from the actual 
direction may be detected in Figure 24. These areas may either be sheltered from 
or exposed to the prevailing direction of storm motion more than the smoothed 
coastal direction would suggest. Differences between these coastal directions on 

75 



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76 



Che Gulf coast may be large enough to cause significant differences in 
frequencies of landfalling tropical cyclones obtained from the direct-count 
method. The effect of the coastal orientation on the frequency count can be 
illustrated by differences in frequencies between the north-south segment of the 
southern portion of the west coast of Florida and the east-west segment of the 
Florida Keys. Because of the coastal orientation, the west coast of Florida is 
subject to landfalling storms from the southwesterly direction, while the Florida 
Keys are at risk from both the southwesterly and southeasterly directions. The 
coastal extensions discussed in Section 6.2.1 helped in analyzing the data near 
the southern tip of Florida. 

Other areas that required special attention are the Cape Hatteras area and the 
Apalachee Bay area. The treatment of a discontinuity in the track count at Cape 
Hatteras was discussed in Chapter 5 (sec. 5.3). Assessing the frequency with 
which tropical cyclones struck the coast along the Gulf of Mexico was more 
complicated than for the Atlantic coast because of the small angle between 
prevailing track directions and the coast, on the one hand, and varying coastal 
directions on the other hand. In order to treat these problems in the Gulf, we 
also made use of the track-density method in which storm paths are considered 
independent of coastal orientation. For a detailed discussion of this approach, 
see the Appendix in TR 15. 

6.2.2 Discussion of Results 

Figure 27 reveals that the range of occurrence of landfalling tropical cyclones 
over a 100-yr period varies from a minimum of 0.1 storms per 10 nmi of smoothed 
coastline near Boston, Massachusetts, to a maximum of 2.2 in the middle of the 
Gulf coast of northwest Florida and the Florida Keys. A frequency of close to 
2.0 storms per 10 nmi per 100 years appears to the south of Galveston, Texas. 
Highest frequency of landfalling tropical cyclones on the east coast is in 
southern Florida, and a comparatively high frequency appears to the south of Cape 
Hatteras, North Carolina. The frequency of entries drops off rapidly from Miami 
to Daytona Beach, Florida and from Cape Hatteras northward to Maine, except 
around Long Island. 

6.2.2.1 Areas of High Entry Frequencies. 

6.2.2.1 (a) Northwest Florida. The high frequency of storm entries along the 
northwest Florida coast near St. Marks suggests that this stretch of the coast is 
a favorable crossroad for tropical cyclones that pass east of the Yucatan 
Peninsula and those that recurve in the Gulf of Mexico. This coastal region is 
also vulnerable to Atlantic storms that cross the Florida Peninsula. 

6.2.2.1 (b) South Florida. A maximum in landfalling storm frequency appears 
near the tip of the Florida peninsula and along the Florida Keys. The 

southernmost portion of this area is exposed to both Atlantic and Caribbean 
hurricanes. Generally, tropical cyclones strike the east coast of south Florida 
from an east-southeasterly direction - a predominant direction for Atlantic 
hurricanes before recurvature. The west coast of south Florida is vulnerable to 
tropical cyclones moving in a northeastward direction after recurvature. The most 
frequent areas of recurvature in the month of October have been near the Bahamas 
and in the northwestern Caribbean (Cry 1965). 



77 



6.2.2.1 (c) Upper Texas Coast. The comparatively high frequency along the upper 
Texas coast is partially caused by the predominantly westward-moving storms in 
Che Gulf of Mexico during the early hurricane season. Only six storms have 
recurved and moved northeastward (away from the southern Texas coast) during the 
months of June, July, and August since 1901. These early season storms accounted 
for more than half the total number of storms that struck the Texas coast. 

6.2.2.1 (d) Cape Hatteras. The high frequency of storm entries just south of 
Cape Hatteras, North Carolina (1.6 storms per 10 nmi per 100 years), is the 
combined result of the number of northeastward moving storms that reentered the 
North Carolina coast after exiting the east coast of Florida and Georgia in 
addition to hurricanes of Atlantic origin that moved in a northerly direction 
after recurvature. Almost 90 percent of the storms entered the North Carolina 
coast, south of Cape Hatteras, in a northwesterly to a northeasterly direction. 

6.2.2.2 Areas of Low Entry Frequencies. The frequency of storm entries is less 
than 1 per 10 nmi of coastline per 100 years over the northern section of the 
east coast from a point some 50 nmi north of Cape Hatteras northward to the 
Canadian border and also in the vicinity of Daytona Beach, Florida. The 
significantly lower frequency of entries north of Cape Hatteras, North Carolina, 
is easily understandable. With a few exceptions, hurricanes recurving south of 
Cape Hatteras either enter the North Carolina coast or move northeastward away 
from the United States mainland. 

6.2.2.2 (a) East Coast. Colon (1953) has shown the locus of points of highest 
frequency of recurvature for different months of the hurricane season. 
Hurricanes off the east coast of the United States frequently recurve between 
latitudes 2 7° and 2 9°N during the months of July and September. For the other 
months of the hurricane season, recurvatures occur at latitudes farther south, 
following the shift of the subtropical ridge (Alaka 1968). The northern limit of 
hurricane recurvature at about 2 9°N appears to coincide with an area of minimum 
frequency of landfalling hurricanes along the east coast. Hurricane Dora of 
September 1964 was the only hurricane that struck the northeastern Florida coast 
in recent years. 

6.2 .2 .2 (b) Gulf Coast. The relative minimum in storm entry frequency along the 
west coast of Florida (compared to the mid-Gulf coast and the southern tip of the 
Florida peninsula) can be explained by the prevailing westward motion of 
hurricanes of Atlantic origin. The relatively low frequency of storm entries 
(before 1985) along the Louisiana coast west of the Mississippi Delta is most 
likely due to sampling variability. The inclusion of storm data for the 1985 and 
1986 hurricane seasons which were not included in this study would have increased 
the entry frequency for this area. 

6.3 Frequency of Exiting Tropical Cyclones 

6.3.1 Analysis 

The freauency of exiting tropical cyclones was defined by a subjective smooth- 
ing of 50-nmi segment coastal crossings. These counts were obtained from the 
storm track information previously cited. A total of 152 tropical cyclones exited 
the Atlantic coast and 20 from the Gulf coast during the period 1871-1984. The 
shape of the coast, relative to storm tracks, and meteorological considerations 
were taken into account in the smoothing. For storms exiting the coasts of 

78 



Florida, consistency in frequency and direction of movement was maintained with 
the frequency of landfalling storms on the opposite coast. The objective 
smoothing technique was not used in this analysis because the observed data are 
closely related to the geographical features of the coasts and because of 
physical considerations (such as direction of storm motion). For these reasons, 
the smoothing of sampling variations of exiting storms that concentrated in these 
areas of the Atlantic coast was done subjectively, taking into account 
meteorological factors. 

6.3.2 Results and Discussion 

Figure 2 8 shows the smoothed frequency distribution of exiting tropical 
cyclones. This curve indicates high frequencies along the coasts of northern 
Florida and Georgia and along the North Carolina coast north of Cape Hatteras. 

6.3.2.1 Gulf Coast. The comparatively few exiting storms along the northern 
portion of the west coast of Florida agrees with the decrease of landfalling 
storms northward along the Atlantic coast of Florida. A local maximum of exiting 
storm frequency occurred near Fort Myers, Florida. 

6.3.2.2 Atlantic Coast. The maximum frequency of exiting storm occurrence ap- 
pears near Jacksonville, Florida, near milepost 1800, with 3 storms per 100 yr 
per 10 nmi of the smoothed coastline (see fig. 28). The frequencies 
decrease southward with 2.2 storms/100 yr/10 nmi near Daytona Beach, 
1 storm/100 yr/10 nmi near West Palm Beach, and 0.3 storms/100 yr/10 nmi near 
Miami, Florida. The frequency diminishes rapidly north of Jacksonville. Higher 
values appear between Cape Hatteras, North Carolina, and Cape Henry, Virginia. 

Many exiting storms along the Atlantic coast originally were eastward-moving 
storms in the Gulf of Mexico. They can also be traced to storms that recurved 
over the Gulf or over the Florida peninsula south of the 29th parallel and moved 
northeastward north of the subtropical ridge. This last group accounts for the 
high frequency of exiting storms over the northeastern portion of the Florida 
peninsula. The concentration of exiting storms just north of Cape Hatteras and 
Cape Cod reflects the orientation of the coastline and the comparatively high 
counts of entering storms south of these capes. 

6.3.2.3 Application in Tide-Frequency Analysis. The treatment of exiting storms 
in tide-frequency analysis for the area north of Cape Hatteras was considered by 
Ho and Tracey (1975). They noted that grouping the parameters into fewer class 
intervals was sufficient for storm-tide computations because exiting storms pro- 
duced lower tides. They concluded that exiting storms made little contribution 
to the overall storm-tide frequencies. Figure 2 9 (from Ho and Tracey) is a graph 
of tide frequencies at Wright Monument, North Carolina, for several classes of 
storms. Curve 'd f shows the computed frequencies of exiting storms contributing 
little to the total tide frequencies. Such minimal contributions from exiting 
storms can be attributed to lower intensities associated with them and from 
dynamic ocean conditions associated with exiting storms. All things being equal, 
exiting storms give smaller surges than landfalling storms. Speed of storm 
motion works inversely for surge generation between exiting/landfall storm. 

Sensitivity tests should be conducted to determine whether omission of the con- 
tribution of exiting storms could affect the desired level of accuracy of the 
overall storm-surge frequencies. Exiting storms on the Florida coasts should be 
considered because of their generally higher frequency of occurrence and stronger 

79 



— "EASTPORT, ME. 



— 30ST0N, MASS. 



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.CAPE HATTERAS, N.C. 



— CHARLESTON, S.C. 



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Figure 29. — Tide frequencies at Wright Monument,' North Carolina, for several 
classes of storms: (a) landf ailing, (b) alongshore, (c) inland, and 
(d) exiting hurricanes and tropical storms; (e) winter storms; (f) all storms 
(from Ho and Tracey 1975>. 

intensities due to limited overland reduction as they move across the relatively 
narrow Florida peninsula.' For estimating exiting storm intensities, the reader is 
referred to Chapter 10 for consideration of overland tilling; rates and Chapter 11 
for application procedures. 

6.4 Frequency of Alongshore Tropical Cyclones 

6.4.1 Analysis 



The frequency estimates for tropical cyclones that bypassed the coast were 
based on the same maps and data period used above. A count was made of storms 
intersecting 5-nmi intervals along lines drawn perpendicular to a smoothed 
coastline centered at each of the coastal locations (A to Z) in Figure 30. The 
same storm may have been counted several times as it moved parallel to the 
coast. The cumulative track counts along each of the 2 6 lines normal to the 
coast were plotted against the distance from the coast. A smooth curve was then 
fit to the data on each of these freauencv Dlots. 




Figure 30. — Accumulative count of hurricane and tropical storm tracks passing tbe 
coast at sea (1871-1984). Based on counts along heavy dashed lines shown 
projected normal to coast. 



32 



The frequency distributions were smoothed subjectively both along the coast and 
perpendicularly outward. These results are shown on Figure 30 by isolines of 
accumulated number of storm tracks bypassing the coast at sea for the 
period 1871-1984. We then read from the map accumulated track counts at discrete 
distances of 10, 20, 30, 50, 75 and 100 nmi from the coast and plotted them as 
alongshore profiles. Additional track counts and frequency plots were made at 
close intervals near areas where the alongshore profiles fluctuated greatly 
because of either a geographic protrusion or a concave coastline. Analysis was 
then undertaken to obtain a set of smooth frequency curves for the Atlantic and 
Gulf coasts. The resultant curves are shown in Figures 31 and 32 depicting the 
accumulated storm track counts in storms per 100 years at selected distances off 
the Gulf and Atlantic coasts, respectively. 

6.4.2 Results and Discussion 

Figure 30 reveals that the maximum concentration of alongshore storms occurred 
off Cape Hatteras, North Carolina. Fewer than five tropical cyclones bypassed 
within 50 to 80 nmi off the coasts of northwest Florida, Alabama, and Mississippi 
and within some 100 nmi of the Texas coast. The higher values off the 
Mississippi Delta may be caused by geographic protrusion. There is a high 
frequency of bypassing storms off the coast of Cape Hatteras for the same reason 
that there is a high frequency of landfalling storms south of Cape Hatteras. The 
gradient at a distance of 100-150 nmi off the Atlantic coast indicates that 
storms frequently traverse at some greater distances off the coast rather than 
bypassing near the coast. This may be explained by the existence of the 
semi -permanent high pressure system (the Bermuda High) in the Atlantic and the 
location of the Gulf Stream off the coast. Atlantic hurricanes approaching these 
latitudes tend to recurve along the western edge of the high pressure cell. The 
higher track counts between 100 to 150 nmi off the coast seem to be associated 
with the mean position of the Gulf Stream. Because of the steep gradient of 
bypassing storm frequencies at some distance off the coast, caution should be 
used in determining a representative frequency over finite distance intervals 
from the coast. 

Figure 31 shows a higher number of storms bypassing the Mississippi Delta and 
the southern tip of the Florida peninsula in the Gulf of Mexico. An analysis of 
storm track counts passing through two and a half degree latitude and longitude 
blocks in the Gulf yielded maximum concentration of storm tracks in an area 
extending from south of the Mississippi Delta to western Cuba (diagram not 
shown). This explains the high values shown in Figure 31. The minimum values 
occurred off the Texas coast and the Apalachee Bay area because of the concave 
coastline in those areas which minimized the count of bypassing storms near the 
coast. Figure 32 shows similar peaks and troughs in the alongshore profile of 
bypassing storm frequencies off the Atlantic coast. These extreme values also 
appear to be associated with geographic features of the coastline. 

7. CENTRAL PRESSURE 

7.1 Introduction 

Central pressure (P ) is a commonly used index of hurricane intensity. 
Harris (1959) demonstrated that storm surge height is approximately proportional 
to the central pressure deficit (AP = P - P ), other factors being constant. 
This chapter develops probability distributions of central pressure for tropical 
cyclones along the coast. 

83 




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The data on which we developed the P Q probability distributions for the 
Atlantic and Gulf coasts of the United States have been collected in Tables 1 
through 3. Original sources of data are described in Section 2.2. Revisions 
were made in P data from TR 15 where we verified suspect data not accepted in 
previous reports and, in a very few cases, as an analysis judgment after 
reviewing all the data. A description of the data analyses was included in 
Section 2.3, and revised hurricane central pressures were listed in Table 4. 

Tables 1 through 3 list parameters of all storms with a central pressure less 
than 982 mb (29.00 in.) that crossed the Atlantic and Gulf coasts or passed 
within 150 nmi on the seaward side of the coast. The criterion that central 
pressure be less than 982 mb was based on the consideration that the computed 
magnitude of cyclostrophic wind using this pressure value (as described in 
sec. 2.3.1) is approximately the wind speed required for classification as a 
hurricane . With central pressure available for an average of less than one 
hurricane per year for the period of record for each coast (Gulf and Atlantic), 
the data in Tables 1 through 3 form a limited sample. 

7.2 Analysis 

Cumulative probabilities of hurricane P were determined from tabulated values 
listed in Tables 1 through 3 for overlapping zones, generally centered 50 nmi 
apart along the coast (see fig. 1). The lateral extent of the zone over which 
the data were pooled was 400 nmi along the Atlantic coast, and 500 nmi on the 
Gulf coast. We used a shorter distance along the Atlantic coast because 
latitudinal variations were more important than along the Gulf coast. The 50-nmi 
criterion was modified in areas where the data were sparse. 

On the Atlantic coast, between the mouth of Chesapeake Bay and eastern Long 
Island, the overlapping 400-nmi zones were separated by 100 nmi, and a single 
zone was used from Long Island to the Canadian border. Near the southern tip of 
Florida, hurricanes that passed near Dry Tortugas, and those that crossed the 
Florida Keys, together with Atlantic coast hurricanes were used to determine the 
probability distributions of P at locations on the Florida Keys. The cumulative 
probability curves, thus obtained, were used in the extension of the Atlantic 
coast along the Florida Keys (see fig. 2 5). 

In southern Florida, along the Gulf coast, the overlapping 500-nmi zones were 
centered 100 nmi apart (instead of 50 nmi). Hurricanes that pass the Florida 
Keys and make landfall in western Florida usually become weaker as they approach 
the coast. Parameters for hurricanes passing the Florida Keys are listed in 



Following the criteria used by NHC, hurricanes are defined as tropical storms 
with winds 64 kn or greater. We realize that there have been storms with 
hurricane-force winds and central pressures as high as 990 mb south of 3 5°N. The 
982-mb criterion was used to put definite bounds on the data sample. In our 
statistical analysis, cumulative probability curves for central pressure are 
extended to cover the full range of hurricanes and tropical storms. 



86 



Table 1 and their characteristics near the time of landfall are given in 
Table 3a. As discussed in Section 7.3.2.1, P Q values tend to be higher north of 
Cape Sable. Treatment of the data near the southern tip of Florida was handled 
differently because of the break at milepost 1415 (see sec. 6.2.1 and fig. 2 5). 
In determining the cumulative probabilities for P Q at coastal reference points 
1350 and 1400 (near Cape Sable), we used P values for 6 hurricanes observed near 
Dry Tortugas instead of the weaker intensities measured near landfall points at 
some distance north of the points of interest. This was done to minimize the 
biasing influence of the large number of generally weaker storms to the north. 

Tables 1 through 3 include only hurricanes with P below 982 mb. However, the 
track count on which the storm frequency (chapt. 6) is based includes tropical 
cyclones of both hurricane and tropical storm intensities. In the application of 
hurricane climatology, frequency of a representative, clima tologically specified 
hurricane of given characteristics is the product of the frequency of all storms 
and the probability of a storm having those particular characteristics. In order 
to ensure a higher leveJL of consistency in our analysis, we expanded the central 
pressure probability distribution to include weaker hurricanes and tropical 
storms, in the manner described below. 

The first step in the analysis of central pressure data was to construct 
cumulative probability curves for each 400- or 500-mile zone. The magnitude of 
central pressure versus probability of occurrence was plotted. Determining the 
probability to be assigned to a data point is commonly referred to as determining 
the plotting position. A plotting position may be expressed as a percent from 
0-100. Probability plotting of hydrologic or meteorologic data requires that 
individual observations or data points be independent of each other and that the 
sample data be representative of the population. 

Gumbel (1958) proposed five criteria for plotting position relationships. 
Several plotting relationships have been presented by Chow (1964). Benson (1962) 
in a comparative study of several plotting position relationships found, on the 
basis of theoretical sampling from extreme value and normal distributions, that 
the Weibull relationship provided estimates that were consistent with 
experience. The Weibull plotting position formula meets all five of the criteria 
proposed by Gumbel. An evaluation of plotting position formulae is included in 
Appendix C. All of the relationships give similar values near the center of the 
distribution, but they vary in the tails. In TR 15, the Hazen plotting position 
formula was used to assess the probabilities. One objection to the Hazen plotting 
position is that the return period for the largest event is twice the record 
length. In the present studv, the Weibull relationship was used in assessing the 
probabilities of all parameters. This plotting position relationship can be 
expressed as: 



X 100 



where p is the probability expressed as a percent of the total number of storms, 
n, and m is the rank from lowest to highest. To get n for all tropical cyclones, 
the count of central pressures (up to 982 mb) was adjusted similar to TR 15, 
using the ratio of hurricanes to the total number of tropical cyclones based on a 
direct count of storm tracks. The upper part of the curve for each graph is ex- 
tended smoothly to 1003 mb at the 100-percent level to arbitrarily represent 





CENTRAL PRESSURE Cm»> 

Figure 33.--Cuaulative probability carve of central pressure of hurricanes 
landfalling within (a) 250 ami of mi 1 epos t 250, near Corpus Christi, Texas, and 
(b) 200 ami of milepost 1600, near Vero Beach, Florida- 
tropical cyclones with central pressure greater than or eaual Co 982 mb. 
Examples of cumulative frequency curves for two coastal zones are shown in 
Figures 33a and 33b. The first is centered near Corpus Christi, Texas and Che 
second near Vero 3each, Florida. 

It should be noted chad the best fit cumulative probability curves were not 
always the most consistent solution for successive 50-nmi increments. The 
Question of how to deal with an outlier in an extreme value distribution analysis 
is always debatable. The central pressure determined for engineering design 
hurricanes (called standard project hurricanes) along the Atlantic and Gulf 
coasts by Schwerdt et al. (1979) was used extensively as a guide in analyzing the 
lower end of the cumulative probability curves for central pressure (see fig. 2.1 
of Schwerdt 's report). In the example given in Figure 33b, central pressure data 
which was used in plotting; the cumulative probabilitv curve for milepost 1600 



near Vero Beach, Florida 



included 



value of 892 mb from the 193 5 



hurricane, 



Earlier studies (e.g., Schwerdt et al. 1979) indicated that a 



hurricane with such a low P would have approached the intensity of a "probable 

maximum hurricane" with a probability of occurrence as much as an order of 

magnitude less than 0.1 percent. Undoubtedlv, this ? value would be considered 

o 
an outlier for the purposes of our analyses. In treating this outlier, more 

weight was given to this storm in the analysis for the Florida Keys, where the 

hurricane made landfall, than at Vero Beach, Florida. The decrease in intensity 

of a "standard project hurricane" from the Florida Keys to Vero Beach was 3lso 

used as a guide in the analvsis. 



88 



Using the smoothed set of cumulative probability curves of minimum central 
pressure, we read off the 1-, 5-, 15-, 30-, 50-, 70, and 90-percentile points for 
each increment and plotted then as alongshore profiles. Analysis was then under- 
taken to obtain a set of curves representing a consistent view of the probability 
distribution of P for the Atlantic and Gulf coasts. The resultant central 
pressure values at selected percentiles for each increment were smoothed using 
the same weighting function employed in Chapter 6 (see sec. 6.2.1.1). 

The relative infreauency of hurricanes near the Canadian border and of P data 
near the Mexican border forced us to subjectively adjust the results of the 
objective smoothing in these end areas. A discontinuity in the analysis with re- 
spect to all but the uppermost class interval was found to exist between the 
chain of Florida Keys and Cape Sable. This was a result of the geographical 
features associated with the tip of the Florida peninsula. Gulf storms striking 
the southern tip of Florida are generally weaker than those moving from the east 
and striking the Atlantic coast of southern Florida and the Keys. Treatment of 
this area was discussed in Section 6.2.1. 

7.3 Results 

An inspection of Figures 34 and 35 reveals that there is an overall increase in 
central pressure from south to north, a well-known fact, caused, in part, by 
decreasing water temperature toward the north. Distinct minima ranked in order 
from lowest pressure at the 5-percent level are found on 1) the tip of the 
Florida peninsula, 2 ) at the Texas-Mexico border, 3) near Louisiana's Mississippi 
Delta, 4) at the South Carolina-North Carolina state line, and 5) over the 
southern New England coast. 

The primary maximum occurs near the (until recently) sparsely populated coastal 
area west of Cross City, Florida (mile 1,100 in fig. 34). Secondary maxima lie 
near the mouth of Delaware Bay (mile 2,400 in fig. 3 5), and near Jacksonville, 
Florida (mile 1,800 in fig. 3 5). The Jacksonville maximum exceeds the Delaware 
Bay maximum for the higher percentile levels. Pressures also rise northward 
along the upper New England coast. 

Reasons for the increase in central pressure from south to north include the 
entrance of colder and drier air at low levels, which destroys the upward slope 
of the isotherms from outside to inside the circulation and decreases the 
amount of energy available to the storm. According to Riehl (1954), jet streams 
at high levels which are detrimental to tropical cyclones are stronger and more 
common in temperate latitudes. Riehl states that "the arrival of the equatorward 
margin of a westerly jet stream at high levels will destroy a [tropical cyclone] 
circulation rapidly since it favors upper convergence, entrance of cold air 
aloft, subsidence, and drying." 

7.3.1 Pressure Minima 

7.3.1.1 South Florida Minimum. The lowest accepted sea-level barometer reading 
(892.3 mb) , not including tornadoes, in the Western Hemisphere occurred at Long 
Key, Florida, in the hurricane of September 2, 1935. This contributed to the 
south Florida minimum. 



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7.3.1.2 South Texas Minimum. Hurricane Beulah (92 3 mb) , the third most intense 
storm (in terms of P ) included in this study, struck the Port Isabel area of 
Texas in September 1967. Hurricane Carla (931 mb) and the Galveston hurricane of 
September 1900 (936 mb) , two other notably severe hurricanes, struck the Texas 
coast between Matagorda and Galveston Islands. There is no reason why Carla or 
the Galveston storm would not have been at least as strong if they had struck the 
south Texas coast. If we look at storms outside the bounds of the main area of 
interest in this study, Hurricanes Janet and Allen also lend strong support for 
the south Texas minimum. Janet brought a P of 914 mb to Chetumal, Mexico (18°N) 
in September 1955 (Dunn et al. 1955). Allen had the lowest central pressure 
(899 mb) ever observed in the western Caribbean while passing through the Yucatan 
Channel on September 7, 1980 (see append. A). 

7.3.1.3 Carolinas and Southern New England Minima. The two lowest tropical 
cyclone central pressures observed along the coasts of Georgia, South Carolina, 
North Carolina and Virginia, occurred during the passage of Hurricane Hazel 
(1954) and Helene (1958). Hazel struck the coast near the North Carolina-South 
Carolina state line. Helene aimed her winds at the same area but turned away to 
the northeast a few hours before the center would have made landfall. In the 
Carolinas and in southern New England where the coast projects eastward, there is 
increased exposure to north-northeastward moving cyclones, some of which, like 
Hazel and Helene, can be of great intensity. 

7.3.1.4 Mississippi Delta Minimum. This minimum was caused principally by 
Hurricane Camille (1969), and its effect is most prominent in the lower 
percentiles. Even though Camille passed east of Louisiana on her way to the 
Mississippi coast, the minimum appears near the mouth of the Mississippi River 
because this portion of the coast is further south (lower latitude). The data at 
the 1-percent level indicate a well-defined minimum; the analysis of the 
5-percent curve in Figure 3 4 was lowered to provide continuity with the 1-percent 
curve. 

7.3.2 Pressure Maxima 

7.3.2.1 Cross City, Florida, Maximum. The lowest central pressure recorded in a 
hurricane entering the northern Gulf coast of the Florida peninsula was 958 mb in 
the storm of September 1950, which entered the coast near Cedar Key. This is not 
nearly as low as hurricane central pressures observed on the mid-Gulf coast 
(Mississippi, Alabama, and the Pensacola area) and on the southwest coast of 
Florida to the south. Is an extremely low P here less likely clima tologically 
or is this simply a sampling variation during the period of record? Present 
indications suggest that there is a real variation and the 1- through 15-percent 
curves in Figure 34 reflect this judgment. 

Our judgment was based on the following. A good many storms have paralleled 
the west coast of Florida close to shore from the Keys northward. Although the 
eyes of these hurricanes remained over water, substantial amounts of air entering 
the storm at the surface had trajectories over the Florida peninsula. Miller 
(1963) has shown that sensible heat is lost from a parcel of air as it travels 
overland. His calculations for Hurricane Donna (1960) show that the surface 
inflow over land is essentially a moist adiabatic process, which leads to the 
hypothesis that, since the major portion of the eastern semicircle of an 
alongshore west Florida hurricane is over land, a portion of the storm's surface 
latent and sensible heat source is removed, the equivalent potential temperature 

92 



of the surface air is lowered, and the radial gradient of equivalent potential 
temperature at the surface is weakened. Movement of a storm out of tropical 
waters can further weaken the gradient. The Labor Day hurricane of 193 5 is a 
good example of what can happen when an intense hurricane leaves the Florida Keys 
and heads up the west coast of Florida. After crossing Long Key with a central 
pressure of 892.3 mb (2 6.3 5 in.), the hurricane brushed Cape Sable and paralleled 
the west coast of Florida for about 30 hours before entering the coast near Dead 
Mans Bay. By then, the storm had weakened to minimal hurricane intensity. The 
air mass north of the hurricane and surface water temperatures had remained 
essentially constant as the storm skirted no more than 50 nmi off the coast for 
those 30 hours. 

Although the area has not experienced a severe storm in over 100 years, it 
should be noted that the Cross City area is exposed to hurricanes moving in from 
the southwest. For a storm moving from this direction, the land effect would not 
be significant. For example, a hurricane could develop over the Bay of Campeche, 
attain great strength over the central Gulf, and then aim its destructive winds 
directly at the area as in the storm of October 1842 (Ludlam 1963). Figure 34 is 
intended to combine these possibilities. 

7.3.2.2 Delaware Bay Maximum. The strongest tropical cyclone to move inland on 
the New Jersey coast during this century was a minimal hurricane (Sept. 1903) 
with central pressure above 982 mb. Storms heading north-northeastward over the 
Delmarva peninsula after having entered the coast at a point farther south are 
more common, but these storms have usually filled to a considerable degree by the 
time they reach Delaware Bay. The raw data have been deliberately undercut in 
the Delaware Bay area because our method of data analysis is more sensitive to 
landf ailing storms than to bypassing storms. Most of the hurricanes affecting 
this part of the coast pass offshore before striking or bypassing the southern 
New England coast, but it is possible that they could turn into the Delmarva-New 
Jersey coast. These storms have central pressures comparable with landfalling 
storms of southern New England. Therefore, in an attempt to provide the best 
estimate of the underlying population and to ensure consistency along this 
section of the coast, the curves for the Delaware Bay area reflect both the raw 
data and the possibility of more intense storms striking the coast. 

7.3 .2 .3 Jacksonville Maximum. The P probabilities achieve another high point 
along the northeast coast of Florida. Again, the shape of the coastline has an 
effect. The direction of the coastline is from 160° to 340° (measured from 
north) in this region. When a storm recurves sufficiently to miss the southeast 
coast, it usually misses the northeast coast. Until 1964, the city of 
Jacksonville was unique in that it was the only major city on the Atlantic coast 
south of Connecticut that had never sustained winds of hurricane force in modern 
times. Hurricane Dora spoiled this fortuitous record in September 1964, lashing 
the Jacksonville area with 82-mph winds and demonstrating that Jacksonville was 
not immune from hurricanes. 

7,3*2.4 Northern New England Coastal Maximum. P Q rises steadily going from 
southeastern Massachusetts northward to Canada. The "cold wall" of the Labrador 
Current contributes to this effect. During August, the month of warmest sea- 
surface temperatures, water temperatures average between 65° and 70°F from Long 
Island to Cape Cod. Along the coast of Maine during the same month, the 
temperature is in the upper 50 's - cold enough to give any tropical cyclone an 
extratropical character. 

93 



8. RADIUS OF MAXIMUM WINDS 

8.1 Analysis 

Cumulative frequencies of R's included in Tables 1 through 3 for the same 
overlapping zones, centered 50 nmi apart, as used for the P analysis were 
analyzed. R's for southern Florida were treated in the same way as pressure. 
The same hurricanes were used for both P and R. For each 400- or 500-nmi 
coastal segment, the R values were plotted on cumulative frequency graphs. The 
percentages were determined by the plotting position formula (see sec. 7.2 and 
append. C). Examples of the frequency analysis for specific coastal segments are 
shown in Figure 3 6. Greater freedom was taken in analyzing the cumulative 
frequency curves of R, and the final coastal variation of the probability 
distributions, than with P Q , because the R data were considered less reliable. 
3ecause data were sparse along the northern portion of the Atlantic coast, the 
cumulative frequencies were developed using both landf ailing and bypassing 
storms. 



account for tropical storms that were not included in the analysis. Tropical 
storms, especially weaker ones, often have no well-defined R, and when they do, 
it can frequently be as much as a hundred miles from the apparent storm center. 
Assigning values of R to such storms would be haphazard, at best. Only 
hurricanes (those in tables 1-3) were considered in the frequency analysis of R 
along the coast. The R values were determined near the location where P 
applies. 

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Figure 3 6. —Cumulative probability curve of radius of aaximum winds for 
hurricanes laodfailing within (a) 2 50 nmi of mlepost 250, near Corpus Christi, 
Texas, and (b) 2 00 nmi of milepost 1600, near Vero 3each, Florida. 



94 



Five discrete probability levels were chosen to portray the results of the 
analysis. The coastal variation of R for the Gulf coast and the Atlantic coast 
is shown in Figures 37 and 38, respectively. The data along the west coast of 
Florida and along the Atlantic coast were limited and were only used to guide 
analysis of the final probability distributions. In these areas, the final 
results reflect a higher level of meteorological judgment. 

8.1.1 Gulf of Mexico 

When the five percentiles for each 50-nmi increment along the Gulf coast were 
plotted and analyzed, the resulting curves (fig. 3 7) depicted a trend of 
increasing R's with latitude, which is consistent with previous studies 
(e.g., Weather Bureau (1957), NHRP 33). Data proved to be too sparse to obtain 
cumulative frequencies of R for the central Texas coast southward. The five 
curves were extended smoothly down the coast to Mexico (about 2 4°N), keeping in 
mind that as we proceeded southward along the coast the value of R should not 
increase with decreasing latitude. 

8.1.2 Atlantic Coast 

Cumulative frequency variation of R along the Atlantic coast as shown in 
Figure 38 displays increasing R with latitude. There were only eight 
observations of R north of Virginia. The smoothing procedure discussed in 
Section 6.2.1.1 was not applied for these latitudes; rather, subjective smoothing 
was used to extend the curves to the Canadian border. 

8.2 Evaluation of the Analysis 

Because of a few additional storms and due to revisions made to several R 

values previously used in TR 15, our analysis resulted in somewhat different 

probability estimates for R than in TR 15. The majority of the revisions were 
decreases in R values. 

8.2.1 Gulf Coast 

8.2.1.1 Florida and Mexico Minima. As mentioned above, there is a variation of 
R with latitude, and, as expected, minima occur on both the eastern and western 
edges of the Gulf of Mexico portion of Figure 37. For example, with the 
exception of Hurricane Camille (1969), an R less than 14 nmi has not been 
observed over the central Gulf coast, while four hurricanes with R's less than 
14 nmi have affected the western and eastern rims of the Gulf. The analysis 
shows moderately lower values on the western rim of the Gulf compared to the same 
latitude on the eastern rim and agrees with NHRP 33, which shows the same trend. 

8.2.1.2 Mississippi-Florida Panhandle Maximum. The northernmost extension of 
the Gulf coast is at Mobile Bay. From what has been discussed so far with regard 
to variation of R with latitude, it is reasonable to expect the maximum in this 
general area. 

8.2.2 Atlantic Coast 

The curves in Figure 38 reflect the fact that the radius of maximum winds tends 
to increase with latitude between the Florida Keys and Canada. The five probabi- 
lity curves attain their greatest slope between coastal Georgia and the Cape 

95 



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97 



Hatteras area. It is in these latitudes that hurricanes most often pass from a 
tropical to a temperate environment, and it is in this region where one would 
expect R to show its greatest increase for the reasons discussed in 
Section 8.3. The slope of the lower probabilities curves change less between 
Georgia and Cape Hatteras because there are a few storms with small R in the data 
sample. 

8.3 Radius of Maximum Winds for Intense Hurricanes 

Observations indicate that hurricanes with very large R's are of moderate or 
weak intensity. In hurricanes moving northward in the Atlantic and becoming 
extratropical, R tends to become larger and more diffuse and P generally 
rises. Data from intense hurricanes of record (see table 16 and fig. 14) 
indicate that the most extreme hurricanes (P less than 92 mb) tend to have 
small R's. The question of interdependence of P and R was discussed in Chapter 
4. We recommend that an R value of 13 nmi be used for hurricanes with P in the 
range of 908-92 mb, and R = 9 nmi be used with P rt less than 908 mb. 



9. SPEED AND DIRECTION OF STORM MOTION 

9.1 Speed of Storm Motion 

Data for the speed of storm motion is discussed in Section 2.5. Included in 
these data are a few subtropical storms. We chose to include them since they 
also have the ability to produce storm surges. 

9.1.1 Forward Speed of Landf ailing Tropical Cyclones 

9.1.1.1 Analysis. Cumulative frequencies of forward speed for landf ailing 
tropical cyclones were determined for the same overlapping zones used for both P 
(sec. 7.2) and R (sec. 8.1). As indicated in Section 2.5, both T and 9 could be 
reliably determined for tropical storms as well as hurricanes, thus increasing 
the sample size. Cumulative probability curves of forward speeds were determined 
using Weibul's plotting position formula (see sec. 7.2). Figure 39 shows 
examples of the cumulative frequency analysis of raw data at two points along the 
coast (near Corpus Christi, Texas and Vero Beach, Florida). Percentage values at 
each 50-nmi location were determined from analyses such as Figure 39 for 5-, 20-, 
40-, 60-, 80- and 95-percent levels. The values were then analyzed to ensure 
consistency along the coast. The resulting curves are shown in Figures 40 and 
41. 

9.1.1.2 Results and Discussion. Figures 40 and 41 show that tropical cyclone 
speed generally increases with northward progression of each storm, especially 
after recurvature to a northerly or northeasterly direction. The upper 
50 percent of forward speeds increases from 11-17 kn near Daytona Beach, Florida, 
to 35-53 kn at the northern extent of the United States' Aclantic coastline. 

Overall, there was a marked increase in values of T along the west coast of 
Florida as compared with the variation shown in values of TR 15. In this study, 
we omitted hurricanes prior to 1900 that had been used in TR 15. This was done 
to ensure a consistent sampling period for all parameters (P , R, T and 9). 
Before finalizing this decision, however, we examined the effect of omitting 
storms prior to the turn of the century. We found that there were no significant 

98 



- 60- 





10 1S 20 25 

?0RWA*D SPEED (kn) FORWAP.0 SPEED (kn) 

Figure 39.-- Cumulative probability curve of forward speed of tropical cyclones 
landf ailing within (a) 2 50 ™i of ailepost 250, near Corpus Christi, Texas, and 
(b) 2 00 nmi of milepost 1600, near Vero Beach, Florida. 



differences in the probability distribution of speed for hurricanes by this 
truncation of the period of record. TR. 1 5 had based its speed distribution on 
hurricanes only. To provide a sample that was consistent with the storms used 
for Che direction distributions, and to increase the sample size, the speeds of 
tropical storms were used in determining the speed distribution. 

The substantial increase in the speeds in the higher percentile levels along 
the west coast of Florida (see fig. 40) was due, not to the change in period of 
record, but to the addition of tropical storms. Between coastal reference points 
900 to 1300, 12 storms with speeds greater than 2 kn were added to the data 
sample. All were less than hurricane intensity. Storms that exceed 2 kn at 
these latitudes generally have become embedded in a broader-scale circulation 
that usually leads to these higher translation speeds. These same oe teorological 
conditions involve recurvature, usually into an environment associated with 
horizontal temperature gradients that create conditions that are not favorable to 
the thermal circulation associated with strong hurricanes (see discussion in 
sec. 7.3.2.1). Therefore, the faster translation speeds appear to be associated 
with weaker storms. However, the small number of storms and high degree of 



99 






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101 



variability from storm to storm precluded us from establishing whether a joint 
probability relation actually exists, let alone what form the relation might 
take. Inclusion of these tropical storms also leads to discontinuities in the 
speed distributions between the west and east coasts of southern Florida for all 
but the lowest percentiles. 

9.1.2 Forward Speed of Bypassing Tropical Cyclones 

Observations of bypassing storms are more limited than for those storms 
striking the coast, especially for storms from earlier years. Additionally, the 
frequency of occurrence of bypassing storms, subject to the criteria in this 
study, is lower than for landfalling storms. Given the high degree of natural 
variability of tropical cyclones and the limitations just mentioned, we felt it 
would be unlikely that we could develop an adequate probability distribution for 
the speed of bypassing storms. Consideration of meteorological factors affecting 
the speed of storm motion suggests that there is likely to be little difference 
in the speed distribution between landfalling and bypassing tropical cyclones. 
The speed is primarily dependent on conditions of the larger-scale meteorological 
environment. In general, the controlling circulation patterns that affect the 
speed are not sensitive to coastal orientation, the factor that leads to the 
segregation of landfalling and bypassing storms. We recommend using the speed 
distribution for landfalling storms as a reasonable approximation for bypassing 
storms* 

9.2 Direction of Storm Motion 

9.2.1 Direction of Storm Motion for Landfalling Tropical Cyclones 

9.2.1.1 Analysis. Tropical cyclone tracks compiled by Cry (1965) and updated 
track charts (Neumann et al. 1981) were used in summarizing the directions of 
storm motion. Directions of landfalling tropical cyclones were measured at the 
time they crossed the coast. Cumulative frequencies of the entry direction for 
overlapping 200-nmi zones (100 nmi either side of the central point) were used in 
plotting cumulative probability curves at 50-nmi intervals along the Atlantic and 
Gulf coasts. In TR 15, cumulative frequencies were counted for overlapping zones 
of 75 nmi on each side. In both cases the zones along the coast were smaller 
than those used for the other three parameters (P , R and T) because the landfall 
directions are totally dependent on coastal orientation which can change 
significantly over relatively short intervals. The smaller zones minimized 
pooling inconsistent directions. We used storm data since 1900 in the present 
study instead of the longer period used in TR 15. We believe the decrease in 
sample size due to a shorter observational period is partially compensated by the 
increased number of storms taken from a somewhat larger sampling area. 

In areas where the coastal orientation changes significantly within 100 nmi of 
the point of interest, the direction of entry with reference to the coast was 
taken into consideration. For example, a storm that crossed the coast from 2 50° 
near Key West would not be counted as a landfalling storm for another point on 
the Florida Keys, some distance to the east. In areas where the coastline turns 
abruptly, frequency counts were taken over shorter distances. Because of 
insufficient data north of Cape Hatteras, analyses there were made over larger 
distance increments. 



102 




105 125 145 195 

DIRECTION (dog. Tom north) 



35 105 125 145 1 95 195 

DIRECTION (dog. Tom north) 
direction of aotion of tropical 



Figure 42.— Cumulative probability curve of 

cyclones landf ailing within (a) 100 nmi of milepost 250, near Corpus Chris ti 
Texas, and (b) 100 nmi of milepost 1600, near Vero Beach, Florida. 



Cumulative probability curves for direction of storm motion for landfalling 
tropical cyclones were constructed using the Weibul plotting position formula 
given in Section 7.2. Figure 42 shows examples of these curves for two coastal 
locations near Corpus Christi, Texas, and Vero Beach, Florida. Each of the 
cumulative probability curves was divided into class intervals, and the values at 
selected percentiles were analyzed for three sections along the coast: the Gulf 
coast (fig. 43), and the Atlantic coast south (fig. 44) and north (fig. 45) of 
Cape Hatteras. 

9.2.1.2 Results and Discussion. The direction of landfalling storm motion is 
closely related to the coastal orientation curve because the definition of 
landfalling restricts the storm direction data selection, exiting and alongshore 
storm motions being excluded. Under the influence of the easterly circulation of 
the lower latitudes (the Azores-Bermuda high) the tracks of most storms in the 
tropics is westward. There is a tendency for these low latitude storms to drift 
slowly northward at the western end of the high pressure system. As the storms 
drift toward higher latitude, they come under the influence of westerly winds and 
recurve northeastward. 



103 



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i — i — i — r 



t — i — r 



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'Id '3d3AW *ld 



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—XL '13SVSI lHOd 



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104 



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105 




25 



ia 



29 



2, 



DISTANCE (nmi X I C 

Figure 45. — Same as Figure 43, but for Che Atlantic coast north of Cape Hatteras. 

As indicated in preceding paragraphs, data sampling for the present analysis 
departed slightly from chat used in TR 15. The analvzed results generally agree 
with Che previous study. On Che Gulf coast, 50 percent of Che scorns occurring 
between coasCal reference points 900 and 1300 anpeared Co have greater southerly 
and easterly components than previously determined in TR 15. This difference may 
be attributed Co Che data samples of different time oeriods. Thirty-four storms 
occurring prior to 1900, with directions from 200 to 270° were not included in 
Che present analysis. 

9.2.1.2 (a) Gulf coast Figure 43 shews smoothed profiles at selected oer- 
centiles for direction of moCion for landfalling tropical cyclones for the Gulf 
coast. As expected, Che tropical cyclones striking Che west coast of Florida 
come from the souChwesC direction and those striking Che Texas coasC are 
generally from Che southeast. Along the mid-Gulf, coastal areas are vulnerable 
to storms approaching from both southeast and southwest. 



106 



9.2.1.2 (b) East coast, south of Cape Hatteras. Figure 44 confirms that for 
la ndf ailing storms near Miami, Florida, the predominant direction of storm motion 
is from the east or southeast. In the vicinity of Daytona Beach, Florida, there 
is higher percentage of landfalling storms coming from the south and southeast. 
North of the Florida-Georgia state line, the percentage of north to 
northeastward moving storms increases gradually northward, which reflects the 
increasing number of recurving storms. This group of landfalling storms 
includes recurving tropical cyclones of Atlantic origin and storms that exited 
the Florida coast and may have reentered the coast south of Cape Hatteras. More 
than 50 percent of the landfalling tropical cyclones near Cape Hatteras are 
north-northeastward moving storms. 

9.2.1.2 (c) East coast, north of Cape Hatteras. For the period since 
publication of TR 15 (1974-84), only two storms made landfall north of Cape 
Hatteras. The directions of motion for these two storms were consistent with 
those used in TR 15. Given the very small number of storms affecting this part 
of the coast, we believe that no changes to the earlier analysis were necessary 
for this stretch of the coast. Figure 45 has been taken from TR 15 for areas 
north of Cape Hatteras, North Carolina. The stretch of coast south of Cape 
Henry, Virginia, is vulnerable to landfalling tropical cyclones coming mainly 
from the easterly directions; the coastal orientation excludes the northeastward 
moving storms from the landfalling category. Tropical cyclones striking this 
part of the coast from the northeast have generally been weak. Figure 45 also 
reveals that tropical cyclones striking the coast east of New York consist mostly 
of northward to northeastward moving storms. 

9.2.1.3 Areas of Discontinuous Direction Profile. The directions of landfalling 
storm profiles along the east coast are not continuous in the vicinity of Cape 
Hatteras, North Carolina and Cape Cod, Massachusetts, because of abrupt turning 
of the coast. The probability distribution of landfalling storm direction and 
its relation to P and T for Cape Hatteras area was discussed in Section 5.4. 
For the Cape Cod area, it is advisable to use the direction distributions from 
the south and west of the eastern extremity of the cape (lower milepost 
number), since the maximum wind region of a hurricane lies to the right of the 
hurricane track. The values indicated for Cape Sable (fig. 43) may be used as 
representative for hurricanes striking the mainland coast of Florida Bay. 

9.2.2 Direction of Storm Motion for Bypassing Tropical Cyclones 

Bypassing storms, by definition, do not strike the coast in the vicinity of 
interest. Variation of coastal orientation and the restriction imposed by the 
definition make specification of a generalized distribution of directions 
impossible. For practical computations, we recommend assigning a direction 
parallel to a tangent to the coastal point of interest for bypassing storms, with 
the general motion from east to west along the Gulf coast facing south, and for 
coasts such as Texas, Florida and along the Atlantic, the general direction 
should be from south to north. 



107 



10. ADJUSTMENT OF HURRICANE INTENSITY FOR FILLING OVERLAND 

10.1 Introduction 

The tropical cyclone is a thermally driven circulation in which the vertical 
flux of sensible and latent heat is the primary source of energy for both its 
formation and maintenance. One of the factors that diminishes hurricane 
intensity is the increased dissipation of kinetic energy by friction overland. 
In a steady-state hurricane, the frictional dissipation of kinetic energy near 
the core of a hurricane is approximately balanced by the energy supplied by 
sensible and latent heat. Overland, the heat sources are greatly reduced or may 
be lacking altogether. Hence, the energy balance between heat and frictional 
dissipation is upset after the hurricane moves overland. It has been suggested 
by Bergeron (1954) and Palmen (1956) that the removal of the sensible heat source 
(hence also the removal of the latent heat source) is the most important factor 
which contributes to the filling process overland. Miller (1963) confirmed the 
earlier work of Bergeron (1954) and others in stating that filling stems 
principally from the reduction of equivalent potential temperature (0 ) of the 
rising air around the hurricane core. Miller also noted that filling due to 
surface friction was of minor importance compared to the removal of the oceanic 
heat source. 

Palmen and Newton (1969) state that "Owing to the removal of the oceanic heat 

source in the inner region, the baroclinity is reduced since the air ascending in 

the inner cloud wall now has somewhat lower 9 . As a result, the outward radial 

e 
wind component in upper levels is reduced. The previous balance between the mass 

inflow is thus temporarily disturbed and pressures rise." 

In this chapter the term "filling" is used in the generally accepted sense. As 
discussed by Petterssen (1956), filling of a center of low pressure refers to an 
increase in the central pressure. Petterssen further distinguishes deepening and 
filling from intensification and weakening: while the former terms apply to the 
pressure, the latter apply to the pressure gradient. Changes in intensity or in 
pressure gradients are not dependent entirely on changes in central pressure. 
Nevertheless, it has been generally assumed that there is a high degree of 
correlation between the two factors (e.g., Hess 1945). Recent studies on inner 
core structure of mature hurricanes generally support this assumption. Most of 
the studies on Atlantic hurricanes based on reconnaissance flight data since the 
1940's have focused on the inner core region (within 1° latitude radius). There 
is a scarcity of upper air data between 2-3° from the center. Frank and 
Gray (1980) used compositing techniques to determine an average radius and 
frequency of 30-kn winds around tropical cyclones. Merrill (1984) found no 
significant correlation of the radii of outer closed isobars with core intensity 
in a comparison of large and small tropical cyclones. Weatherford (1985) 
examined flight-level wind data obtained by reconnaissance aircraft flown into 
tropical cyclones in the northern Pacific during the period 1980-82. She showed 
that the outer strength (as measured by the magnitude of winds between 1°- and 
3°-latitude radius of the storm center) is highly correlated with the extent of 
30-kt surface winds, while the core intensity was a far more variable feature. 

10.2 Index for Overland Filling 

In defining clima tological hurricane parameters for this study, we assumed a 
steady-state hurricane moving on a constant course during the time period 
required for storm surge computation. Strictly, these assumptions cannot be 

108 



carried through to determine a filling rate for hurricanes over land. However, 
transient phenomena of the hurricane core will not be considered. After the 
center of a hurricane crosses the coast, the hurricanes' central pressure rises 
faster than the change in peripheral pressure and the pressure deficit 
decreases. The decreasing intensity of the hurricane affects the level of storm 
surge, especially in bays and estuaries. It has been shown that the coastal 
surge and the surge producing forces in bays and estuaries vary proportionally 
with pressure deficit (e.g., Harris (1959), Ho and Myers (1975)). These 
surge-producing forces in bays and estuaries are, mainly, the propagation of open 
ocean surge into the bay and wind setup. The open coast storm surge increases 
with increasing kinetic energy of the wind which acts on the water surface, other 
factors being held constant. In a mature hurricane, the kinetic energy of the 
wind is approximately proportional to the pressure deficit. Hence, the coastal 
surge and the propagation of the open coast surge into a bay are approximately 
proportional to the pressure deficit in a hurricane. The second major factor in 
the bay and estuary response is wind setup. The magnitude of the wind setup 
effect is also proportional to the kinetic energy of wind for given conditions 
and, thus, is also approximately proportional to the concurrent pressure deficit. 

Having considered the cause and effect of filling of hurricanes, it is logical 
to select pressure deficit as an index in defining the rate of filling 
overland. The advantages in selecting such an index is its direct and simple 
application to numerical surge models. Its application is, however, restricted 
because the averaging process used in the analyses tends to ignore the 
extremes. Recognizing that wind profiles in individual hurricanes do not always 
vary with the change in central pressure, the resultant rate of filling is best 
utilized in an idealized hurricane model. The user is cautioned against using an 
average filling rate for individual hurricane case studies for the purpose of 
replicating storm surge levels, especially in bays and estuaries. 

10.3 Previous Observational Studies 

Hubert (1955) observed that filling is most pronounced in the innermost region 
of the hurricane. Malkin (1959) stated that both filling and decrease in 
intensity proceed at a lesser rate when the ratio of water to land of the 
underlying surface increases along the track. Malkin analyzed the change in 
central pressure after landfall of 13 selected hurricanes and evaluated the 
average change in pressure gradient after landfall. Schwerdt et al. (1979) 
analyzed eight selected hurricanes which occurred during the period 1957-70 with 
central pressure less than 949 mb. They accepted the previous data and analyses 
made by Malkin and developed the filling rates in terms of reduction in wind 
speed for 3 different zones along the Gulf and Atlantic coasts of the United 
States. Jarvinen et al. (1985) suggested a quadratric filling rate of central 
pressure for hurricanes along the Texas coast and stated that the largest 
intensity changes occurred in the most intense storms within the first 6 hours 
after landfall. 

10.4 Analysis of Data 

In this chapter, the decrease in hurricane intensity after landfall was 
determined by using the ratios of pressure deficits at specified times after 
landfall (AP ) and the pressure deficit at the time of landfall (AP ). The 



109 



pressure deficit was obtained by subtracting the central pressure (P Q ) from the 
peripheral pressure (P n )» These ratios give the percentage decrease in intensity 
and, thus, a rate of filling for hurricanes overland. 

In order to determine the pressure deficit, an analysis of P and P must be 
made for the duration of the storm over land. Values of P n were estimated from 
3-hour ly weather maps. For P , graphs were constructed showing sea-level pressure 
readings from stations with available continuous pressure records during the time 
period when a hurricane approached and passed by that station. These pressure 
readings and corresponding distances from the storm center were used in composite 
pressure-distance profiles analyzed at 3-hour intervals for a duration of 
24 hours after landfall. These profiles were then extrapolated to the storm 
center, yielding estimated central pressures at various times. 

Observations are taken at regular reporting stations as well as by many private 
individuals and corporations for their own uses. In some cases, this material is 
filed with the National Climatic Data Center (NCDC), NOAA's Cooperative Reporting 
Network. Additionally, after many severe storms, surveys are made to obtain 
supplementary data that are not routinely collected. With improvement of the 
observational network, analyses of observed data have proven to yield fairly good 
estimates of central pressure. These analyses, supplemented by analyzed synoptic 



Available data were plotted and a profile was fit to the data by eye. This 
allowed meteorological considerations to influence the resulting profiles. 
Figure 46 is an example of central pressure-time profiles for Hurricanes 
Frederick (1979) and Alicia (1983). Both hurricanes struck the Gulf coast; 
Frederick made landfall near the Alabama-Mississippi state line, while Alicia 
entered the coast just south of Galveston, Texas. 

10.5 Filling Rates by Region 

Table 19 shows a list of selected hurricanes which were analyzed individually 
to estimate the decrease in hurricane intensity after landfall. The data sample 
of 23 hurricane events was separated into three groups, based on the location 
where each hurricane crossed the coast. These regions are shown in Figure 47. 
Region A is the area along Gulf coast from Port Isabel, Texas, to Apalachicola , 
Florida, region B, the coast of Florida south of 29°N, and region C, the Atlantic 
coast from South Carolina to Rhode Island. Hurricane Camille, listed with other 
hurricanes in region A, was both intense and small in size, and had the steepest 
filling rate within the first 6 hours after landfall. Its central pressure rose 
from 909 mb to 965 mb in 6 hours, an average increase of more than 9 mb per 
hour. Camille stands out as a special case, presumably representative of the 
most intense storms. Since our hurricane sample indicates that there is a 
tendency for the more intense hurricanes to fill more rapidly, we have chosen to 
provide separate filling rates for extreme hurricanes. 

For region A, filling rates were determined for each of the six Gulf hurricanes 
since 1971, following the procedures outlined in Section 10.4. Figures 48 a and 
b show the variation with time after landfall of filling rates of hurricanes 
listed in part A of Table 19. The filling rate is the ratio of pressure deficit 
at specified times (t) after landfall (AP ) to the pressure deficit at the time 
of landfall (AP ), or AP /AP . The filling rate for Hurricane Camille was 
adopted from analyses made in an earlier study (Schwerdt et al. 1979). Filling 

110 





1005 


I 


! 1 




I 1 | " ~ 


S 


995 


- 







jgS* 


LU 


985 


- 






^**r _ 


3 
CO 

CO 

LU 
lT 
Q. 


975 


_o 









LU 
> 
LU 


965 











< 

LU 














955 


jT 






• PRESSURE - OISTANCE PROFILES 
STATION PRESSURE 




945 C 


1 


' 1 




(a) 

i i i 



9 12 

TIME fhr) 



15 



13 



1000 



1 990 



980 



970 



960 - 



- 


! 


1 


1 


1 I 1 


■„.**% 


- 









^S* 


- 




/ 




- 











• PRESSURE-DISTANCE PROFILES 
& RECONNAISSANCE AIRCRAFT 
STATION PRESSURE 

(b) 




! 


i 


1 


1 i 1 



12 



TIME Chr) 



Figure 46. — Pressure profiles after landfall for (a 
September, 1979 and (b) Hurricane Alicia, August, 1983. 



1 3 



Hurricane Frederick. 



Ill 




Figure 47. — Map showing geographical regions used Co study filling rates. 



L 12 



Table 19. — Selected landf ailing hurricanes (192 8-1983) used to estimate overland 
filling rates. 



No. of 
Storms 



Hurricane 



State of 
Landfall 



Region 



11 



Aud rey 
Carla ( 
Betsy ( 
Camille 
Celia ( 
#Edith ( 
•/Carmen 
#Eloise 
//Frederi 
#Allen ( 
//Alicia 



(1957) 

1961) 

1965) 

(1969) 
1970) 
1971) 
(1974) 
(1975) 
ck (1979) 
1980) 
(1983) 



Louisiana 

Texas 

Louisiana 

Mississippi 

Texas 

Louisiana 

Louisiana 

NW Florida 

Mississippi-Alabama 

S. Texas 

Texas 



(Gulf coast from 

Apalachicola, FL 

westward) 



Sept. 17, 1928 
Sept. 15, 1945 
Aug. 27, 1949 
Donna (1960) 



S. Florida 

S. Florida 

S. Florida 

S. Florida 



(Florida 
south of 29°N) 



Sept. 21, 193 8 
Sept. 15, 1944 
Carol (1954) 
Hazel (1954) 
Gracie (1959) 
Donna (1960) 
//Belle (197 6) 
#David (1979) 



New York 
New York 
New York 
North Carolina 
South Carolina 
New York 
New York 
Georgia 



(Atlantic coast 

from South Carolin, 

northward) 



# Indicates storms since 1971 



rates for other hurricanes prior to 1971 determined by Schwerdt et al. were 
checked for consistency by using observed minimum pressure data as previously 
discussed. Minor changes were made whenever warranted. 

The filling rates at selected time intervals for the 11 hurricanes listed in 
Table 19 for region A were averaged to develop a filling rate for hurricanes of 
lesser intensity. Separate filling rates for more intense hurricanes were 
estimated by taking into consideration this average filling rate and the extreme 
filling rate associated with Camille. Intense hurricanes were arbitrarily 
defined as storms with AP greater than 85 mb, which have approximately the same 
intensity as category 5 hurricanes according to the Saf fir/Simpson scale 



(Saffir 1977) 



Figure 49 shows the filling rate curves for hurricanes with AP. 



less than or equal to 85 mb, AP equal to 100 mb, and AP equal to 110 mb. These 
curves have been used to develop the pressure deficits in part (a) of Table 20. 
Linear interpolation between values in Table 20 should be used instead of 
recourse to Figure 49 to assure a higher degree of accuracy and consistency. 



113 




11 



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\ \ \\ x. 

X \ \ \ x 

\ *V x X 

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115 




22. 



oiiva 



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- 2 



116 



Table 20. — Changes in hurricane pressure deficits due to overland filling 



Time After 
Landfall 

(hr) Pressure Deficit (mb) 



(a) Gulf hurricanes, west of Apalachicola, Florida 



40 60 80 85 90 95 100 105 110 



2 


34 


51 


68 


72 


76 


78 


80 


81 


82 


4 


30 


44 


59 


63 


66 


67 


68 


69 


70 


6 


26 


40 


53 


56 


58 


59 


60 


61 


62 


8 


22 


34 


45 


48 


50 


51 


52 


53 


54 


10 


20 


30 


40 


42 


44 


45 


46 


47 


47 


12 


18 


27 


36 


38 


39 


40 


41 


41 


42 


14 


16 


24 


32 


34 


35 


36 


36 


36 


36 


16 


14 


21 


28 


30 


31 


32 


32 


32 


32 


18 


12 


19 


25 


26 


27 


28 


28 


28 


28 



(b) Florida hurricanes, south of 29°N 



40 60 80 85 90 95 100 105 110 
38 57 75 80 85 88 90 91 92 
36 54 70 75 79 81 82 83 84 



6 34 


51 


67 


71 


75 


76 


77 


78 


79 


8 32 


48 


63 


67 


71 


72 


73 


74 


75 


10 30 


45 


59 


63 


67 


68 


69 


70 


71 


12 28 


42 


56 


60 


63 


64 


65 


66 


67 


14 26 


40 


53 


56 


59 


60 


61 


62 


63 


16 25 


37 


50 


53 


55 


56 


57 


58 


59 


18 24 


35 


47 


50 


52 


53 


53 


54 


55 


(c) Atlantic 


hurricanes, north of 


Georgi a-Sou th 


Carolina 


state 


line 


40 


60 


80 


85 


90 


95 


100 


105 


110 


2 36 


54 


72 


76 


81 


86 


90 


94 


99 


4 32 


49 


65 


68 


73 


77 


81 


85 


89 


6 28 


44 


58 


61 


65 


68 


72 


76 


79 


8 25 


39 


51 


54 


57 


60 


64 


67 


70 


10 22 


34 


44 


47 


50 


53 


56 


59 


61 


12 19 


29 


38 


41 


43 


46 


48 


51 


53 



14 17 25 34 36 38 40 42 44 46 
16 15 22 30 31 33 35 37 39 ' 40 
18 13 19 26 27 29 30 32 34 35 



117 




<]|<3 ' 6 



Figure 50, — Comparison of filling rates for various hurricanes crossing the 
Florida peninsula and Che filling curve for region B from Schwerdt 
ec al. (1979). 

There were no additional storms that affected region B since 1971. The average 
filling rate curve determined by Schwerdt et al. (1979) was adonted after 
checking for consistency by comparing A? t /A? ratios for several hurricanes. Mo 
attempt was made to obtain separate filling rate curves for each of these 
hurricanes because data was scanty. Figure 50 shows a plot of these ratios at 
various times after landfall and the filling rate curve for region B from 
Schwerdt et al. It is again recommended that filling rates be obtained from the 
values in Table 20b by linear interpolation. Figure 51 shows filling rate curves 
for selected oressure deficit levels in region B. 

Figure 52 shows the filling rate at various times after landfall for Hurricane 
Hazel (1954) and Gracie (1959). These two hurricanes entered the Atlantic coast, 
crossed the Carolinas, and recurved towards the north. Filling rates for a 12-hr 
period after landfall are shown in the figure because both hurricanes became 
extratropical soon after that period of time. The changes in intensity during 
their extratropical stage would not be representative of hurricanes. Only the 
rate of weakening for the first 12-hr period, as indicated by the solid line, was 
used in this analysis. Figure 52 also shows the rate of weakening for Hurricane 
David (1979) after entering the coast just south of Savannah, Georgia. The 
obvious difference between the curves reveals that David had a much slower 



113 




119 




Ol<3 - 6 



Figure 52. — Variation with tine after landfall of filling rates for Hurricanes 
Hazel (1954), Gracie (1959), and David (1979). 

filling rate than those of Hazel and Gracie. This can be partially explained by 
che fact that David traveled inland, parallel Co the coast, with half of the 
cyclonic circulation of che storm remaining over water. The heat supply from the 
underlying sea acted to minimize the filling process. For this reason, David was 
not used in obtaining an average filling rate for Atlantic coast hurricanes. 

Figure 53 shows a plot of filling rate versus time after landfall for 
hurricanes which crossed the shores of Long Island, New York and the New England 
states. Data obtained during the first 12-hr period after landfall were used in 
Che analysis because Chese hurricanes were fast moving storms. In a 12-hr period 
after landfall, they would have either moved across the United States border into 
Canada or become extratropical. The average filling rates for these hurricanes 
agree fairly well with the filling curve for Hurricanes Hazel and 
Gracie (fig. 52). Combining both sets of data, we obtained the average filling 
curve as shown in Figure 54. Since region C has not experienced any extreme 
hurricanes, this curve was adopted to represent the filling rates of landfalling 
hurricanes of all intensities in this region. Again, linear interpolation from 
Table 20 should be used to determine pressure deficits. 



120 



<3l<3 



< 




1.0 

6 8 

TIME Chr) 

Figure 53. — Variation with tiae of filling races for New England hurricanes. 

10.6 Results 

The lower filling rate curves for regions A and 3 in Figures 49 and 51 ara 
applicable to hurricanes with pressure deficits less Chan or equal to 85 mb at 
the time of landfall. For hurricanes with pressure deficits greater than 35 mb, 
filling rates may be obtained from interpolation of pressure deficit values given 
in Tables 20a and 20b for regions A and B, respectively. There is no separate 
filling rate determined for hurricanes of the most intense category in region C. 



12 1 




122 



The filling rate for region C, shown in Figure 54, was extended to depict 
filling up to 18 hr after landfall, for consistency. One should realize that the 
degree of accuracy decays with increasing time after landfall. The curve for 
region C is also applicable to areas north of Long Island, New York in order to 
include the entire coastline. 

Assuming that the rate of filling is linear for the first 10-hr period after 
landfall, we can draw a straight line joining the point indicating the filling 
rate at 10 hr after landfall and the point of origin for each of the three 
regions. We obtained slopes of .051, .075, and .056 for regions A, B, and C, 
respectively. Linear interpolation of the slopes may be used as an aid to 
develop intermediate curves in estimating appropriate filling rates for areas 
lying between designated regions. 

11. APPLICATION OF HURRICANE PARAMETERS 

11.1 Introduction 

An objective of this report has been to define climatological probability 
distributions of hurricane central pressure (P Q ), radius of maximum winds (R), 
forward speed (T), and direction of motion (9) along the Atlantic or Gulf coasts 
of the United States. In some applications of these data — for example, in flood 
insurance studies — it would be necessary to calculate frequency distributions 
of hurricane-induced surges on the coast by combining the analysis of hurricane 
climatology with the application of a numerical storm-surge model. Also needed 
in such application is the overall frequency with which hurricanes enter the 
coast in terms of strikes per mile per year, or some equivalent unit, within 
certain discrete distances. The landfall point of a hurricane is another 
parameter needed in a surge-frequency analysis. If storm track is parallel to 
the coast, then distance from the coast is needed instead of direction. This 
chapter outlines procedures to be followed in selecting hurricane parameters, 
their corresponding probabilities, and the representative storm tracks and 
frequencies for surge-frequency analyses as currently adopted in flood insurance 
studies. 

11.2 Landfall Point 

The cyclonic wind field of a hurricane usually increases from the edge of the 
storm to the highest value at the radius of maximum winds (R) then rapidly 
decreases to low values near the center. There is usually some asymmetry to the 
approximately circular pattern, with the highest winds on the right side as the 
storm moves forward. From the geometry of the hurricane wind field pattern, the 
maximum shoreward component is experienced at a given coastal site when the 
hurricane center landfalls approximately at distance R to the left. On a 
straight coast with uniform bathymetry, the highest surge along the coast will be 
experienced at this point of highest wind. Variable bathymetry can modify this 
location somewhat. Similarly, a bay experiences the strongest winds from a 
hurricane of given intensity and lateral extent when the storm track is about at 
distance R to the left of the center of the bay, as viewed from the sea. 

In addition to the inverse barometer effect and the convergence of wind 
affecting surge levels near a storm's center, the major driving force for coastal 
surges is the stress of the wind on the water, roughly proportional to the square 
of the wind speed. Average wind profiles show that surface winds of a hurricane 

123 



at a distance five times the radius of maximum winds (5R) from the storm center 
are less than half of its maximum magnitude (Schwerdt et al. (1979), chapt. 13) 
and the magnitude of the corresponding peak surge heights are only about 
2 5 percent of the peak. Except for the most intense storms, hurricane-induced 
surges of any significant level would not affect the coast if the hurricane made 
landfall at a distance exceeding 5R to the left of the point of interest or at a 
distance of more than 3R to the right. The distance 3R is chosen because coastal 
surge heights drop off much more rapidly to the left of the landfall point. 

11.3 Peripheral Pressure 

The linkage between the climatologically-def ined hurricane central pressure 
(P Q ) and the pressure deficit (AP) used in a storm-surge model is the peripheral 
pressure (P n )« p n is used to compute the pressure deficit (AP = P - P ), which 
is a measure of the intensity of a hurricane. P is frequently considered the 
average pressure around the hurricane where the isobars change from cyclonic to 
anticyclonic curvature. This pressure occurs at a distance from the storm center 
near where storm inflow begins and, therefore, has physical meaning. In this 
study, P is used in conjunction with clima tologically determined hurricanes. 
The use of a climatological mean value for P is considered adequate for this 
purpose. 

Schwerdt et al. (1979) described several techniques for evaluating P and 
indicated that there is no significant variation of P with latitude. They 
compiled peripheral pressures for Gulf and Atlantic coast hurricanes with P less 
than 982 mb since 1900. The average value of these given peripheral pressures is 
1013 mb. We recommend that this climatological mean value be adopted as a 
representative peripheral pressure to compute pressure deficits in storm-surge 
frequency analysis. 

11.4 Probability Distributions of Hurricane Parameters 
and Frequency of Occurrence 

This chapter describes the application of hurricane parameters needed to 
calculate storm surge levels on the coast. The assessment of probability 
distributions of these parameters assumes a steady-state hurricane moving on a 
constant course during the time period required for storm-surge computations. The 
averaging process along the Gulf and Atlantic coasts assures a smooth continuous 
variation of individual parameters along the coast. Exceptions to these basic 
assumptions and specific treatment of discontinuities have been discussed in 
preceding chapters. These include frequencies of landfalling tropical cyclones 
for the Florida Keys (sec. 6.2), refinements in alongshore hurricane track counts 
and probability distributions of landfalling storms for the North Carolina coast 
(sec. 5.4), frequencies of exiting storms (sec. 6.3), and filling of storms as 
they pass overland (chapt. 10). The procedure to estimate probability distribu- 
tions of hurricane parameters for exiting storms will be discussed further in 
subsequent paragraphs. 

The probability distribution of P is determined for landfalling tropical 
cyclones (sec. 7.3). There is no reason to believe that the pressure distribution 
of alongshore storms would be different from that of landfalling storms because 
both classes of storms experience an area with climatologically similar atmos- 
pheric and sea-surface conditions. Hence, this probability distribution of P 
can also be applied to alongshore storms. The probability distribution of R is 

124 



assumed to be the same for the landf ailing, bvpassing and exiting categories of 
storms. Probability distributions for direction and speed of storm motion for 
landfalling storms are given in Chapter 9. For alongshore storms, the direction 
is, by definition, assumed to be parallel to the coast and the probability 
distribution of forward speed is assumed to be the same as for landfalling 
hurricanes. 

The frequency of tropical cyclone occurrence is defined as the number of tracks 
per year per nautical mile of a smoothed coast for each of the landfalling and 
exiting categories of storms (chapt. 6). Figure 27 depicts variation of 
frequencies of landfalling tropical cyclones along a smooth coastline. We have 
implicitly smoothed out the coast while smoothing out the accidental landfalling 
points of storms. A stretch of the coast that turns sharply in a direction 
almost parallel to that of the predominant storm motion is less exposed than 
adjacent coastal segments more normal to the track direction. For areas where 
the coast turns abruptly, such as the Mississippi Delta, Apalachee Bay, and the 
tip of Florida, special consideration must be given in using the generalized 
results in this report. An example of the treatment of a discontinuity in land- 
falling storm frequencies at Cape Hatteras, North Carolina, is discussed in 
Section 5.4. In areas where variations of frequencies along the coast are large, 
the effects of the steep gradient of hurricane frequencies along the coast on 
resultant coastal surge frequencies must be considered (see examples given in the 
following section). 

For alongshore hurricanes, the bypassing distance is a significant parameter 
instead of the landfalling point discussed in Section 11.2. The frequency of an 
alongshore hurricane event is treated in the same way as the landfalling storms, 
except that the frequency is defined as the number of storms per year passing 
through a given distance interval along the line perpendicular to the coast. It 
is the counterpart of the frequency per year for landfalling storms multiplied by 
the length of coastal segment, determined by the spacing of storm tracks for 
computations. The application of this is further discussed in the following 
section. Figures 3 1 and 32 depict the variation along the Gulf and Atlantic 
coasts of tropical cyclone tracks bypassing the coast at sea. These figures give 
accumulated track count at selected intervals from the coast. With this 
information, plots of the cumulative count of tracks versus distance from the 
coast can be constructed for any coastal point. Figure 55 is an example of the 
accumulated track count plotted against distance from the coast for Vero 
Beach, Florida. The difference in accumulated track count between two points 
read off the graph gives the number of storms, per 100 years, crossing the given 
distance interval. It is advisable to use small distance intervals near the 
coast, using the selected R values for landfalling storms as a guide. This would 
ensure that the effect of maximum winds on coastal waters would maximize 
generated surge levels. 

The frequency of tropical cyclones bypassing the coast overland is not treated 
as such in this report. First, these storms tend to weaken after traversing over 
land and the surge frequencies resulting from these storms are usually not 
significant (see for example fig. 29). Second, the contribution of this class of 
storms to surge frequencies varies greatly in different localities. Coastal 
surges of significant levels can be produced by such storms in areas near the 
Outer Banks of North Carolina and in the southern portion of the Florida 
peninsula. For the treatment of this class of storms in North Carolina, the 
reader is referred to the report by Ho and Tracey (1975). The North Carolina 

12 5 




40 60 80 

DISTANCE FROM COAST (nmi) 



Figure 55. — Plot of cumulative count of alongshore storms versus distance from 
coast for Vero Beach, Florida {milepost 1600). 



12 6 



study mav be used as a .guide for the Florida peninsula area. A good example of 
these storms in Florida is the hurricane of October 1950 which entered the coast 
of south Miami and moved north-northwestward over the entire length of the 
peninsula. Its intensity weakened to that of a tropical storm after passing near 
Orlando, Florida. Another hurricane that entered the southern tip of Florida and 
weakened rapidly while moving northward is the hurricane of 193 5. It was the 
most intense Atlantic hurricane ever recorded (P = 892 mb while crossing the 
Florida Keys). It weakened to minimal hurricane intensity (P = 960 mb) by the 
time it crossed the northern Florida coast, near 30°N. Hurricanes that move 
northward over the Florida Peninsula seem to fill faster than hurricanes that 
cross the peninsula in a east-west duration. It should be noted that the filling 
rate in Chapter 10 for Florida should not be applied to this class of northward 
moving hurricanes. The treatment of such tropical cyclones passing the coast 
inland needs further investigation. 

11.5 Applications of Profiles of Probability Distributions 
for Hurricane Parameters 

Hurricane parameters for storm-surge frequency computations can be obtained by 
constructing cumulative probability curves for each of the hurricane parameters 
from smoothed alongshore graphs. Table 2 1 itemizes the information needed by the 
user. Items 1-4 are information to be listed for identification. Item 5 lists 
the meteorological information needed for surge-frequency computations and where 
it can be found in this report. Numerical values to be filled in (5a through 5 j ) 
are hurricane parameter values for designated percentiles and frequencies read 
from the appropriate figures for the location (milepost) listed in Item 4. Using 
these values for the designated percentiles, the full range of individual 
parameters of clima tologically possible hurricanes that can make landfall at the 
point of interest can be determined. The cumulative probability curve, thus 
obtained, is then divided into class intervals that can be used in frequency 
computations. 

In storm-surge frequency analysis, landfall points should be selected by taking 
into consideration the lateral extent of the coast affected by an individual 
hurricane. Based on the geometry of the hurricane wind field, as discussed in 
Section 11.2, we recommend that the coastal area of influence for the purpose of 
surge computations be limited to a distance 5R to the left and 3R to the right of 
the point of interest. Hurricane tracks crossing landf ailing points at 10-2 5 nmi 
intervals should be considered in estimating overall surge levels. The computed 
peak surge at the point of interest for a given storm passing along each of the 
selected hurricane tracks is assumed to be representative of a "surge event" that 
could occur within the distance interval (10-2 5 nmi) between two landf ailing 
points. Hence, the selection of track spacing should be guided by (1) the 
alongshore gradient of the bathemetry, (2) the storm size and (3) the 
configuration of coastal areas. For example, tracks spaced at larger distance 
intervals may be specified for a straight coastline with uniform bathymetry while 
computation for storms crossing landf ailing points at close intervals would be 
needed to produce representative surge levels on the shorelines of bays and 
estuaries. To obtain the frequency of this "surge event" multiply the frequency 
of landfalling storms (storms/nmi/yr, given in item 5h of table 2 1) by the 
selected distance interval between landfalling points. 



127 



Table 21 — Summary sheet of information needed from this report for surge- 
frequency computations 



1. Geographic location 

2. Latitude 

3. Longitude 

4. Milepost [fig. 1] 

5. Hurricane parameters 



Central pressure (P ) [fig. 35] 
Pressure deficit (1013-P Q ) 



Forward speed (T) [fig. 41] 

Direction (9) [fig. 44] 

Coastal orientation 

Angle of approach (d-e) 

Radius of maximum winds (R) [fig. 38] 



Percentile 



1 


5 


15 


30 


50 


70 


90 































Percentile 



5 1 20 


40 


60 


80 


95 


1 











Percentile 



5 


16.67 


50 


83.33 


95 











































h. Frequency of landfalling storms 
[fig. 27] 



i. Frequency of exiting storms 
[fig. 28] 



storms/10 nmi/100 yr, or 

storms/nmi/yr 

storms/10 nmi/100 yr, or 

storms/nmi/yr 



j. Frequency of alongshore storms (accumulative counts) [fig. 32] 



Distance from 
coast (nrai) 


Frequency 
(storms/100 yr) 


Frequency 
(storm/yr) 


Frequency within 
distance interval 


10 








20 








30 








50 








75 








100 









128 



After completing the appropriate number of forms for the coastal area of 
interest, the information can be used to reconstruct cumulative probability 
curves for the parameters that describe the clima tologically possible hurricanes 
for each of the selected locations. Intermediate cumulative probability curves, 
if required, may be estimated using linear interpolation. The reconstructed 
cumulative probability curves will provide values for any selected percentile 
within the full range of individual parameters. Intermediate curves will insure 
a smooth transition from one location to the next. 

Table 22a is an example of a completed computation form for storm-surge 
frequency analysis at Vero Beach, Florida (milepost 1600). Tables 22b and 22c 
contain similar information for locations located 50 nmi to the north and south 
of Vero Beach, respectively. Figure 56 shows a plot of cumulative probability 
curves of P for the three locations. Curves for intermediate locations can be 
determined by linear interpolation. It should be noted that the lowest 1 percent 
of P for Vero Beach and the lowest 2 percent of P for the location 50 nmi to 
the south (fig. 56) fall into the intense hurricane category. As discussed in 
Section 4.5, these hurricanes should have an assigned R of 13 nmi. Similarly, 
cumulative probability curves can be plotted for the other parameters. 

Figure 55 shows a plot of cumulative frequency of bypassing hurricane tracks 
versus distance from the coast for Vero Beach. The accumulated track counts for 
selected distances from the coast are taken from Item 5j of Table 22a. A smooth 
line was then drawn by eye joining the data points. From this curve, the 
frequency of bypassing storms within the first 10 nmi of the coast is 0.0170 
storms/yr, the number of storms passing the distance interval of 10-30 nmi is 
(0.0575-0.0170) 0.0405 storms/yr and the track count for the distance interval of 
30-75 nmi is (0.1600-0.0575) 0.1025 storms/yr. Similarly, frequencies within 
other distance intervals may be obtained (e.g., table 23). 

The next step in determining hurricane probabilities requires that the hurri- 
cane parameters be divided into class intervals for the landfalling storms and 
that the mid-point value of each class interval be determined. The size and 
number of intervals cannot be specified a priori, but must involve judgment that 
considers factors that can vary from site to site; an example for P is given in 
Figure 57. It should be noted that Figure 57 shows only the fraction of all 
hurricanes with intensities below certain levels and makes no reference to 
frequency in terms of events per year. For storm-tide frequency computation, 
this continuous distribution could be divided into five class intervals, each 
represented by the pressure deficits at the mid-point of the class interval. 
This computational probability distribution is indicated by the dashed line on 
Figure 57. For computation purposes, the hurricanes are treated as if the most 
severe 1 percent all had pressure deficits of 95 mb, the next 6 percent had a 
deficit of 84 mb, the next 12 percent a deficit of 70 mb, the next 40 percent a 
deficit of 45 mb and the last 41 percent a deficit of 19 mb. These class 
intervals are representative values and their corresponding probabilities are 
listed in Table 23. It is of interest to note that these class intervals are not 
equally spaced. Closer intervals are used for parameters associated with intense 
hurricanes. Higher surge levels produced by the intense hurricanes contribute to 
the 100-yr or higher tide frequencies. Similarly, cumulative probability curves 
for other parameters can be divided into class intervals, and values for 
designated percentiles are listed in Table 23. 



129 



Table 22a — Summary sheet for Vero Beach, Florida 



27° 39» N 



80° 27' w 



1600 



1. Geographic location 

2. Latitude 

3 . Longi tude 

4. Milepost [fig. 1] 

5. Hurricane parameters 



Central pressure (P ) [fig. 35] 
Pressure deficit (1013-P ) 



Forward speed (T) [fig. 41] 

Direction (9) [fig. 44] 

Coastal orientation 

Angle of approach (d-e) 

Radius of maximum winds (R) [fig. 3< 



Vero Beach, Florida 



Percentile 



1 


5 


15 


30 


50 


70 


90 


921 


93 1 


94 5 


958 


977 


990 


997 


92 


82 


68 


55 


36 


23 


16 



Percentile 



5 


20 


40 | 60 


80 


95 


3.5 


6.5 


8.5 


10.6 


13.0 


16.3 



Percentile 



5 


16.67 


50 


83.3 3 


95 


055 


087 


118 


13 5 


153 


020 


020 


020 


02 


020 


03 5 


067 


098 


115 


133 


5.5 


11.0 


18.0 


28.0 


37.0 



h. Frequency of landf ailing storms 
[fig. 27] 



i. Freemen cy of exiting storms 
[fig. 23] 



0.76 



storms/10 nmi/100 yr, or 



0.00076 storms /nmi/yr 

1 .2 storms/10 nmi/100 yr, or 

0.0012 storms/nmi/vr 



j. Frequency of alongshore storms (accumulative counts) [fig. 32 



Distance from 
coast (nmi) 


Frequency 
(storms/100 yr) 


Frequency 
(storm/vr) 


Frequency within 
distance interval 


10 


1.70 


0.0170 


0.0170 (0 - 10 nmi) 


20 


3 .3 


0.033 


0.0160 (10- 20 nmi) 


30 


5.75 


0.0575 


0.0245 (2 0- 30 nmi) 


50 


10.00 


0.1000 


0.042 5 (3 0- 50 nmi) 


75 


16.00 


0.1600 


0.0600 (50- 75 nmi) 


100 


2 4.00 


0.2 400 


0.0800 (75-100 nmi) 



130 



Table 22b — Summary sheet for 50 nmi north of Vero Beach, Florida 



1. Geographic location 

2 . Latitude 

3 . Longi tude 

4. Milepost [fig. 1] 

5. Hurricane parameters 



Central pressure (P ) [fig. 35] 
Pressure deficit (1013-P Q ) 



c. Forward speed (T) [fig. 41] 

d. Direction (0) [fig. 44] 

e. Coastal orientation 

f. Angle of approach (d-e) 

g. Radius of maximum winds (R) [fig. 38] 



Vero Beach + 50 nmi 



28° 30* 


N 


80° 42' 


W 


1650 



Percentile 



1 


5 


15 


30 


50 


70 


90 


92 5 


93 5 


949 


963 


981 


991 


997 


88 


78 


64 


50 


32 


22 


16 







Percentile 






5 


20 


40 60 


80 


95 


3.8 


6.8 


8.8 


11.0 


13.2 


16.5 



Percentile 



5 


16.67 


50 


83.33 


95 


044 


076 


115 


131 


153 


000 


000 


000 


000 


000 


044 


076 


115 


• 131 


153 


6.3 


11.5 


19.0 


28.8 


37.5 



h. Frequency of landfalling storms 0.74 storms/10 nmi/100 yr, or 

[fig. 27] 

0.00074 storms /nmi/yr 

1.65 storms/10 nmi/100 vr, or 



i. Frequency of exiting storms _ _ 

[fig. 28] 

0.00165 storms /nmi/yr 

j. Frequency of alongshore storms (accumulative counts) [fig. 32] 



Distance from 
coast (nmi) 


Frequency 
(storms/100 yr) 


Frequency 
(storm/yr) 


Frequency within 
distance interval 


10 


1.3 6 


0.0136 


0.013 6 (0 - 10 nmi) 


20 


2.41 


0.02 41 


0.0105 (10- 20 nmi) 


30 


4.32 


0.0432 


0.0191 (20- 30 nmi) 


50 


8.2 5 


0.082 5 


0.0393 (3 0- 50 nmi) 


75 


14.10 


0.1410 


0.0585 (50- 75 nmi) 


100 


22 .60 


0.2260 


0.0850 (75-100 nmi) 



131 



Table 22c — Summary sheet for 50 miles south of Vero Beach, Florida 



1. Geographic location 

2 . Latitude 

3 . Longi tude 

4. Milepost [fig. 1] 

5. Hurricane parameters 



Vero Beach 



50 



26° 54' N 



80° 11» W 



1550 



Percentile 



Central pressure (P ) [fig. 3 5' 
Pressure deficit (1013-P ) 



Forward speed (T) [fig. 41] 

Direction (9) [fig. 44] 

Coastal orientation 

Angle of approach (d-e) 

Radius of maximum winds (R) [fig. 3. 



1 


5 


15 


30 


50 


70 


90 


916 


92 7 


941 


955 


974 


989 


996 


97 


86 


72 


58 


39 


24 


17 







Percentile 




5 


20 


40 


60 1 80 


95 


3.4 


6.4 


8.5 


10.5 1 12 .8 


16.2 



Percentile 



5 


16.67 


50 


83.33 


95 


059 


093 


12 


142 


155 


020 


020 


02 


020 


02 


039 


073 


100 


122 


13 5 


5.0 


10.0 


17.5 


28.0 


37.0 



h. Frequency of landfalling storms 
[fig. 27] 



i. Frequency of exiting storms 
[fig. 28] 



0.97 



torms/10 nmi/100 yr, or 



0.00097 storms /nmi/yr 

0.90 storms/10 nmi/100 yr, or 



0.00090 storms /nmi/yr 

j. Frequency of alongshore storms (accumulative counts) [fig. 32] 



Distance from 
coast (nmi) 


Frequency 
(storms/100 yr) 


Frequency 
(storm/yr) 


Frequency within 
distance interval 


10 


2 .34 


0.0234 


0.023 4 (0 - 10 nmi) 


20 


4.02 


0.0402 


0.0168 (10- 2 nmi) 


30 


7.10 


0.0710 


0.0308 (20- 30 nmi) 


50 


12.50 


0.1250 


0.0540 (3 0- 50 nmi) 


75 


18.50 


0.1850 


0.0600 (50- 75 nmi) 


100 


25.80 


0.2580 


0.0730 (75-100 nmi) 



132 





10 










._ — '* 


- 




20 












■ 




30 


- 










- 


s~\ 








'// 








-a 








;/' 






















° 


40 






</' 






- 


j 








* '/' 








5 








* /' 
















'/; 








Ll_ 


50 










- 


UJ 








f At— Vero Beach 








3 




Vero 


Beach + 50-*// 








LU 








/ // 








(V 


60 






/ // 






- 


D 
CO 








//' 

/ // 








10 








/ //-*- Vero Beach-50 








—J 


70 






7 /' 






- 


Q_ 








/ // 
t / ' 

' / ' 










80 






' / ' 
' / * 

f / / 










90 




/ 
/ J 


/ / 
/ 






™ 




/ 


i 


/ 










100 1 










J I i l 





1 5 10 20 30 40 50 60 70 80 90 

EXCEEDANCE PROBABILITY 



95 97 



■99 



Figure 56,-- Cumulative probability curves of ? for designated locations. 

The parameters adopted for Vero Beach, Florida, in Table 23 represent five 
pressure deficit categories, four R categories, three T categories and three 
9 categories. These factors are considered statistically independent except that 
the four R's are not the same for all pressure deficit categories, a small value 
being used with the class interval of most intense pressure deficits in line with 
the discussion in Section 4.5. Thus, in Table 23, the most intense hurricanes 
(1 percent of total count) are assumed to have an R of 13 nmi. The R's for 
weaker storms cover the full range of values. For these storms, the R class 
intervals need not be equally spaced. One needs to consider an appropriate class 
interval for the critical range of R near 3 nmi. This is because of the 
importance of the dynamic effect of winds near R on the surse calculation. For a 
hurricane with constant intensity crossing the continental shelf of average 
width, the induced peak surge reaches its maximum value for R at or slightly 
greater than 30 nmi. Similarly, there exists a critical motion relative to a 
coast that gives the highest possible surge under any given set of conditions. 
The critical speed generally is greater than 2 5 kn. Thus, the fastest moving 
storms, especially if they are large and moving directly toward the coast, pose 
the greatest hazard. Appropriate class intervals should also be designated for 



133 



Table 23. — Tropical cyclone parameters Vero Beach, Florida 



P AP 

(mb) (mb) 



R 

(nmi) 



T 
(kn) 



9 L 
(deg.) 



Pe 



Landf ailing 



918 


95 


0.01 


* 




5.7 


0.30 


040 


0.16 


929 


84 


0.06 


11.0 


0.333 


9.5 


0.40 


088 


0.40 


943 


70 


0.12 


18.0 


0.333 


14.0 


0.30 


112 


0.44 


968 


45 


0.40 


28.0 


0.333 










994 


19 


0.41 















Landf ailing storm frequency = 0.00076 storms /nmi /yr. 

* R = 13 nmi is assigned a probability of 1.0 for P < 920 mb. 



Exiting 



950 


63 


0.07 


13.8 


0.5 


8.8 


0.5 


067 


1.0 


961 


52 


0.12 


23.5 


0.5 


18.0 


0.5 






980 


33 


0.40 














999 


14 


0.41 















Exiting storm frequency = 0.0012 storms/nmi/yr , 



('nmi) 



(storms/vr) 



Alongshore 
R p r T 

(nmi) (kn) 



5.0 


0.017 


13 


.5 


7.0 


.5 


P , AP, and P i are 
the same as those 


15.0 


0.016 


25 


.5 


12.3 


.5 


25.0 


0.024 










for landfalling 


40.0 


0.042 










storms 


62.5 


0.060 













Central pressure (mb) 

Pressure deficit (mb) 

Proportion of total storms with indicated AP value 

Distance from center of storm to principal belt of maximum winds (nmi) 

Proportion of storms with indicated R value 

Forward speed of storm (kt) 

Proportion of storms with indicated T value 

Direction of entry or exit, measured clockwise from the coast (deg.) 



o 
AP = 

p i = 
R = 

p r : 

^: 

Li 

Pq = Proportion of storms with indicated 9, value 
L = Distance of storm track from coast (nmi) 

F = Frequency of storm tracks crossing a line normal to coast 
(storm tracks /yr passing through the interval centered at L) 



134 




SO 40 20 

PRESSURE DEFICIT (rnb) 

Figure 57. — Cumulative probability curve for pressure deficit at 
Beach, Florida. Dashed lines shown selected class intervals. 



Vero 



Che critical range of speed and direction. The direction of approach, 88°, was 
selected (table 23) to represent the most critical ranee of directions which 
would oroduce the highest coastal surge if other factors were the same. 



In Table 23, the most intense landf ailing hurricane class interval (1 percent 
of the total) is assumed to have an R of 13 nmi and one third of each class of 
less intense hurricanes are assumed to have R's of 11, 18, and 2 5 nmi. The ? 
and R categories for landfalling storms given in Table 23 define 13 different 
hurricanes [ 4 (?) Q X 3(R) + (P = 918 and R = 13)]. The probability of each of 
these is obtained by multiplying the respective probabilities in the table. The 
sum of the probabilities of the 13 hurricanes, of course, eauals 1. P and R are 
statistically independent of d and T. Thus, the parameters for landfalling storms 
defines 117 different hurricanes (13 X 3(T) X 3(9)). Each of the 117 discrete 
storms represent a portion of the probability domain, the probability of each 



135 



storm is obtained by multiplying the four parameter probabilities. For example, 
the probability of having a hypothetical hurricane with P = 92 9 mb, R = 18 nmi, 
T = 9.5 kn, and 9 L = 88°, is 0.0032 (0.06 X 0.333 X 0.4 X 0.4). 

11.6 Exiting Tropical Cyclones 

The intensity of exiting storms generally decreases because the overland tra- 
jectory reduces the energy supply (see chapt. 10). Central pressure data observed 
over the ocean in landfalling and alongshore storms may not be used to estimate 
the probability distribution of P Q for exiting storms. Because of insufficient 
data sample size, no attempt was made to construct cumulative probability curves 
of hurricane parameters for exiting storms based on observed data. 

As previously indicated (sec. 6.3.2.3), exiting storms normally contribute 

little to the overall frequencies of storm surges, except for the Florida 

peninsula. Storms exiting the east coast of Florida frequently come from the 

southwest. Plots of cumulative probability curves of landfalling direction along 

the west coast of Florida show a median direction of about 22 7° (from north) 

along most of the coast. The median direction for storms crossing the Florida 

peninsula from the Atlantic to the Gulf varies from 110-13 0° (from north). The 

typical translation speed of these storms is about 10 kn (see figs. 40 and 41). 

Using the median landfalling direction on the opposite coast, and assuming that 

the storm direction remains constant as it crosses the peninsula, a 

representative overland storm track can be determined for exiting storms. The 

next step is to estimate the time it takes the storm to cross the peninsula, 

using the median landfalling speed, which is also assumed constant. This time can 

be used to determine 'filling-rate factors (sec. 10.5) that can be applied to the 

P distribution at the landfall point. The modified P distribution is then used 

o o 

to approximate the P distribution for exiting storms. 

Except for P we assume that there are no changes in other parameters as 
storms crossed the Florida peninsula. Cumulative probability curves developed for 
R, T, and at the point of landfall are applicable to storms exiting the 
opposite coast. For expediency and economic considerations it will usually be 
sufficient to assign two class intervals for each of the R and T distributions 
and four intervals for P (e.g., see table 23). The direction of storms exiting 
the east coast of Florida may be represented by 22 7° from north since the range 
of probable direction of exit is so small. Two class intervals for directions of 
storms exiting the west coast of Florida are recommended by assigning 50 percent 
probability each to the directions of 073° and 116° from north. Because of 
infrequent occurrence of storms exiting north of Tampa Bay on the west coast of 
Florida, it should not be necessary to attempt to define exiting storm parameters 
to the north of this point. 



12. SUMMARY AND DISCUSSION 

This report presents an analysis of the geographical distribution of major 
hurricane and tropical storm factors useful for flood insurance studies. Each of 
these factors influences the ability of the storms to produce storm tides. This 
report provides a climatology of hurricane factors needed for surge-frequency 
analyses and information useful for storm-surge modeling. Because our purpose 
was to develop clima tological data in a probabilistic sense, judicious smoothing 

136 



Table 24. — Data used in this report for probability analyses 



Clima tological 
Characteristic 



Data 
Source 



Application 



Figures 



Storm frequencv Tropical cyclone tracks 

(landfalling. of the North Atlantic 

alongshore, Ocean, 1871-1984 
exiting) 



Tropical cyclones 



27, 28 
31, 32 



Central 
pressure 

Radius of 
maximum winds 



Tables 1 to 3 (hurricanes 
with P Q <982 mb since 1900) 

Tables 1 to 3 (hurricanes 
with P Q <982 mb since 1900) 



Tropical cyclones 34, 35 



Direction and Tropical cyclone tracks of 
speed of forward the North Atlantic Ocean, 
motion 1900-84, 'HURDAT' tape 



Hurricanes 



Tropical cyclones 



37, 3! 



40, 41, 43 
44. 45 



Cumulative probability curves for central pressure, based on hurricane data, 
were extended to include tropical storms. 

was employed along the Atlantic and Gulf coasts and across the frequency spectra 
to eliminate the effect of sampling fluctuations. Results of our analyses are 
given in figures and tables with brief definitions and explanations. The figures 
depicting coastal profiles of probability distributions for selected percentiles 
give ranges of clima tological ly defined hurricane parameters. Users should 
determine for their particular application the critical class intervals within 
these ranges. 

Table 2 4 summarizes the data sources and the classes of tropical cyclones 
represented. These are not the same for the all factors, for the reasons stated 
in the report. 

12.1 Frequency of Tropical Cyclone Occurrences 

The frequency of landfalling, exiting, and bypassing tropical cyclones were 
summarized in Figures 27, 28, 3 1 and 32, respectively. Of the three classes of 
storms, the most significant factor for storm-surge frequency computations is the 
frequency of landfalling storms. Coastal variation of landfalling storm 
frequencies is most rapid along the Atlantic coast of Florida and along the North 
Carolina and Virginia coasts (fig. 27). This steep gradient of hurricane 
frequency contributes to the potential for significant differences in the 
magnitude of resultant coastal surge frequencies in adjacent locations along 
these portions of the coast. Frequencies of alongshore storms are generally 
small (negligible) for most of the Gulf coast and, except for portions of the 
west coast of Florida, contribute little to the overall tide frequencies. High 
frequencies of exiting storms occurred on the Atlantic coast near Jacksonville, 
Florida and just north of Cape Hatteras. Exiting storms generally produce lower 
storm surges and they are usually weaker than landfalling or alongshore storms 



137 



for the same latitudes. Their contribution to the overall storm-surge 
frecuencies is negligible in most cases. Because of coastal orientation, 
frequencies of landf ailing storms are not continuous from Cape Sable, Florida, to 
the Florida Keys. Our treatment of the analysis in this area is discussed in 
Section 6.2 . 

12.2 Probability Distribution of Storm Parameters 

Analysis of the data led to a set of graphs depicting the probability 
distribution of central pressure, radius of maximum winds, forward speed, and 
direction of storm motion. The central pressure distribution (figs. 34 and 3 5) 
is for tropical cyclones and is broken down for illustrative purposes into seven 
probabilit-z levels (percentiles) ranging from 1 to 90 percent. The probability 
levels were selected at intervals sufficiently close for the purpose of 
reconstructing smooth cumulative probability curves and should not be considered 
as a guide in selecting the number of class intervals appropriate for 
computational purposes. 

Probability levels ranging from 5 to 95 percent were selected to depict the 
full range of other parameters (R, T, 9). The distribution for the radius of 
maximum winds (figs. 37 and 38) was derived from hurricane data only, and is 
illustrated for five selected probability levels. The resulting probability 
distribution may be considered applicable for both hurricanes and tropical 
storms. The forward speed distribution (figs. 40 and 41), based on tropical 
cyclones landfalling on the United States coasts, is illustrated for six selected 
probability levels. This distribution is also adopted for alongshore storms, as 
discussed in Section 11.4. The direction of storm motion distribution for 
landf ailing tropical cyclones is illustrated for five probability levels in 
Figures 43 (Gulf) and 44 (Atlantic coast, south of Gape Hatteras). Because of 
the very limited number of storms affecting the Atlantic coast north of Cape 
Hatteras, only three probabilitv levels are given for direction of storm motion 
for this portion of the coast (fig. 45). 

12.3 Independence of Parameters 

The parameters presented in this study can be considered statistically 
independent, exceot for central pressure (P_) and radius of maximum winds (R). 
Limited historical data indicate that hurricanes with central pressure below 
920 mb have small R's. Hurricanes with large R's are nearly always of moderate 
or weak intensity, but not all the weaker storms have large R's. Establishing 
the joint probability of two factors with a degree of reliability racuires a much 
larger sample of data than that available in Tables 1 to 3 . For this reason, we 
specify R values for only the most intense hurricanes (sec. 4.5). 

Observations show that alongshore hurricanes generally move at a faster speed 
than landfalling hurricanes at the same latitude. The differences in forward 
speeds (T) were presumably related to the direction of storm motion, 9, 
(according to TR 15). There was no detectable interrelation between T and 9 for 
landfalling hurricanes found in statistical tests of the present study. The 
small sample size does not allow us to establish any interrelation between T and 
9 for alongshore storms. With increased data in future years, it would be of 
interest to re-examine this rela tionshio. 



133 



It is generally believed that hurricanes striking the Florida Keys from an 
easterly direction are more intense than hurricanes coming from the southwesterly 
direction. The data sample for that area is not sufficient for us to 
statistically establish an interrelation of P and for landfalling storms. A 
similar situation exists in the area north of Cape Hatteras, North Carolina. In 
the latter case, separate P probability distributions were evaluated for 
tropical cyclones coming from the northeasterly and southeasterly directions (see 
chapt. 5). Segregating the sample into subgroups would take care of the inter- 
dependence of P and 9 for this particular area. This approach may be used to 
deal with similar problems in other regions. 



ACKNOWLEDGMENTS 

The authors are grateful for the help of numerous members of the Water 
Management Information Division, Office of Hydrology, National Weather Service, 
during the course of this study. In particular, we would like to thank Helen V. 
Rodgers for invaluable editorial assistance, and Roxanne Johnson who ably 
prepared many of the figures for this report. The guidance and critical review 
of the manuscript by E. Marshall Hansen, Chief of the Water Management Division, 
was especially helpful. 

We would like to thank researchers at the National Hurricane Center, the 
Hurricane Research Division of NOAA's Atlantic Oceanographic and Meteorological 
Laboratories, and the National Weather Service's Techniques Development 
Laboratories for their extremely helpful discussions, both during the formative 
stages of our study, and as work progressed. We also want to thank Dr. Gerald F. 
Cotton of NOAA's Air Resources Laboratory, who advised us on some statistical 
procedures. 

The authors especially want to express their appreciation to the staff of the 
Hurricane Research Division for providing us with data from their files. In 
particular, we wish to thank Mark D. Powell for sharing with us his data 
collections obtained in post-hurricane surveys, and Neil Dorst for preparing 
computer plots of hurricane wind data observed by reconnaissance aircraft. 

Periodic meetings with the staff of the sponsoring agency, the Federal 
Emergency Management Agency, and their consultants, provided us with additional 
insight throughout the preparation of this report. Dr. Frank Tsai of the Federal 
Insurance Agency, Federal Emergency Management Agency, Dr. Chester P. Jelesianski 
of the Techniques Development Laboratory, and Charles Neumann of the National 
Hurricane Center, provided crucial reviews of drafts of this report. These 
reviews were most helpful in improving the quality of the final product. 



139 



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unpublished memorandum HUR 7-97, U.S. Department of Commerce, Silver 
Spring, MD, 45 pp. 

Weatherford, C.L. , 1985: Typhoon Structure Variability. Department of 
Atmospheric Science Paper No. 391, Colorado State University, Ft. Collins, CO, 
77 pp. 

Willoughby, H.E., 1979: Some Aspects of the Dynamics in Hurricane Anita of 1977, 
NOAA Technical Memorandum ERL-NHEML-5, Environmental Research Laboratories, 
National Oceanic and Atmospheric Administration, U.S. Department of Commerce, 
Miami, FL , 30pp. 

Willoughby, H.E., Clos, J. A., and Shoreibah, M.G. , 1982: Concentric Eye Walls, 
Secondary Wind Maxima, and the Evolution of the Hurricane Vortex, Journal of 
the Atmospheric Sciences , Vol. 39, pp. 395-411. 

Willoughby, H.E., 1985: Confirmatory Observations of Concentric Eyes in 
Hurricanes, Extended Abstracts, 16th Conference on Hurricanes and Tropical 
Meteorology, American Meteorological Society, Boston, MA. 



146 



APPENDIX A 

Detailed Analysis of Selected Storms 

A.l Introduction 

Data for storms that have occurred since TR 15 and are included in Tables 1 to 
3 were based on consideration of research work done by others and our own 
detailed analyses. This Appendix provides examples of the analyses leading to 
development of the parameters used in this study. The first storm discussed is 
Hurricane Alicia, which is representative of Gulf storms. We then discuss 
Hurricane David which affected the Atlantic coast. David was also used in 
Chapter 4 to examine the relation between P and R. Finally, we conclude with an 
examination of Hurricane Allen. Allen was used in Chapter 4, and is an example 
of an intense storm undergoing a number of strengthening and weakening cycles. 

A.2 Hurricane Alicia, August 15-21, 1983 

A-2 .1 Introduction 

Hurricane Alicia was the first hurricane since Carla (1961) to cause extensive 
damage in the Houston-Galveston, Texas area (estimated at 1.8 billion [1983] 
dollars). By hurricane standards, Alicia was only a medium sized hurricane that 
reached a minimal category 3 status (based upon the Saf fir/Simpson scale) at 
landfall. Carla was a much larger and more intense hurricane than Alicia, but 
Alicia struck a highly urbanized coastal area. Alicia caused more damage than 
Carla - the estimated total damage of nearly 2 billion dollars is the largest 
dollar damage ever recorded for a hurricane striking Texas. If a hurricane the 
size and strength of Carla were to strike close to the Galveston Bay area today, 
the losses have been estimated to be two to three times more than those caused by 
Alicia (Case and Gerrish 1984). 

While the analyses described in this Appendix can provide useful information on 
a single storm event for calibration of hurricane surge computation using a 
numerical model, the purpose of the analyses was to specify clima tological 
hurricane parameters. These are central pressure, speed and direction of forward 
motion, and the radius of maximum winds. 

A.2 .2 Previous Reports 

The National Hurricane Center provided a description of significant features of 
all Atlantic tropical storms that occurred during 1983, including Hurricane 
Alicia, in the Monthly Weather Review (Case and Gerrish 1984) and in the National 
Summary of Climatic Data (National Hurricane Center 1983). These publications 
also included a smoothed "best" track for Alicia. The NHC publication on annual 
data and verification tabulation for the 1983 Atlantic tropical cyclones (Clark 
and Staff 1984) also includes a list of Alicia's center-fix positions obtained 
by aerial reconnaissance penetrations, satellite images, and land-based radar. 
The hurricane's central pressure, maximum winds and other data observed by 
reconnaissance aircraft are also included in that report. Meteorological data 
collected at data buoy stations in the Gulf of Mexico can be found in the report 
"NDBC Observations During Hurricanes Alicia and Barry, 1983," published by the 
NOAA Data Buoy Center (1984). 

147 



Lambeth (1983) provided a summary of available information about Hurricane 
Alicia. It included maximum wind, minimum pressure, and times of occurrences of 
both, reported from regular reporting stations and other sources, including the 
Texas Air Control Board (6 stations), Houston Regional Monitoring Corporation 
(12 monitoring stations) in the Houston-Galveston area, and the Dow Chemical 
Plant in Freeport, Texas. 

Marshall (1984) used surface windspeeds recorded during the passage of Alicia 
to estimate fastest-mile windspeeds at 10 m above ground and compared these 
speeds with recommended windspeed criteria for the design of buildings and other 
permanent structures. Powell et al. (1984) described the asymmetric character of 
the windfield in Hurricane Alicia and the changes in the winds during landfall. 
They found that the strongest surface and flight-level winds showed a close 
relationship to the precipitation structure of the storm as depicted by radar. 
Willoughby (1985) also described the evolution of Alicia's windfield as the 
hurricane made landfall. 

The Galveston District of the U.S. Army Corps of Engineers (1983) evaluated 
storm damage caused by Alicia and published summaries of hydrologic, meteorologic 
and damage data. Garcia and Flor (1984) compiled coastal and inland tide gage 
data and high-water marks associated with Hurricane Alicia. They also included 
wave data and wave spectra in their report. 

A .2 .3 Sources of Data 

The reports discussed in the previous section were used to the maximum extent 
possible in the present study. We also examined original records to ensure the 
accuracy and completeness of this study and to enable us to provide more detailed 
information on track position, speed, central pressure, etc. This permitted us 
to perform the most comprehensive and detailed analysis yet developed for 
meteorological factors associated with Alicia and important to storm-surge 
modeling. 

The basic information was obtained from the regularly reporting network of 
weather stations operated by NWS, NOAA and the military services. These reports 
are maintained at the National Climatic Data Center in Asheville, North Carolina. 
Supplemental data, available in the NCDC archives, included ship observations, 
radar observations, radiosonde records, reconnaissance flight data and satellite 
observations. 

In addition, meteorological data collected by research aircraft of NOAA' s 
Office of Aircraft Operations (0A0) were processed by computer and stored on 
magnetic tapes at the Hurricane Research Division (HRD) of NOAA's Atlantic 
Oceanographic and Meteorological Laboratory (AOML) in Miami, Florida. This 
information was made available to us for this report. A detailed description of 
the collection of meteorological information by aircraft, including the 
instrumentation, its calibration, and reliabilities, has been included in 
Hawkins et al. (1962). A more recent discussion of the calibration and 
instrumentation of present-day NOAA research aircraft can be found in other 
publications (e.g., Merceret et al. 1980). Availability of airborne research 
meteorological data collected by HRD/AOML are included in Friedman et al. (1982, 
1984). 



148 



A.2 .4 General Meteorological Situation 

The system which developed into Hurricane Alicia on August 17, 1983, initially 
formed in the northern portion of the central Gulf of Mexico. This system 
intensified into a tropical storm around mid-day of August 15 and drifted 
westward for the next 2 4 hours.' Surface pressures were high over the Gulf of 
Mexico and remained high during the early stages of the storm's development. 
Several ships located near the storm reported pressures of 1015 to 1016 mb late 
on the 15th. During this time the storm remained quite small and generated winds 
stronger than usually observed in storms with similar minimum central 
pressures. Alicia turned toward the west-northwest on the afternoon of August 16 
and attained hurricane intensity on the morning of the 17th. Hurricane Alicia 
moved northwestward at the a steady pace and crossed the Texas coast about 30 nmi 
southwest of Galveston at 0700 GMT on August 18. The minimum pressure at the time 
of landfall was 962 mb. Maximum sustained winds of 78 kn were reported by a 
Coast Guard Cutter near Galveston. Alicia maintained its hurricane intensity for 
the 6 hours after making landfall. Maximum winds of 77 kn were reported at 1050 
and 1524 GMT at Pearland, Texas, and 70 kn at 1300 GMT at Baytown, Texas. After 
passing the southwestern suburbs of Houston, Texas, Alicia weakened rapidly and 
moved northwestward over Texas and then northward over western Oklahoma. 

A.2 .5 Detailed Meteorological Analysis 

A primary focus of this study was to analyze in detail hurricane parameters 
used in storm-surge models in order to develop a statistical climatology. For 
this purpose, we analyzed raw observational data. The intent of these analyses 
was to develop specific values of the hurricane's central pressure, radius of 
maximum winds, direction and speed of forward motion, and location of its center 
at various time intervals. Particular attention was focused on the period just 
before and after the hurricane made landfall since this is the time interval most 
critical for storm-surge computation. 

A.2 .5.1 Storm Track, Generally, the analyses of meteorological data are 

weighted toward synoptic-scale motion. The hurricane track, thus obtained, is 
the best estimate of the large-scale motion and not necessarily the most precise 
location of the eye at discrete time intervals. Track differences of a few 
miles, insignificant in determining the large-scale motion, can be significant 
for replicating high water on the open coast and inside bays and estuaries in 
surge-model computations. 

Figure A.l shows the final track determined for Hurricane Alicia from 0000 CST 
(0600 GMT) on August 16 through 1200 CST (1800 GMT) August 18 together with 
locations of meteorological stations used in this report. Except for Baytown, 
the stations are either NWS offices or military installations reporting regularly 
to the NWS. The positions of the storm center are shown at 6-hour intervals. 
The central pressure (mb) and the radius of maximum winds (nmi) are plotted to 
the left of 12-hour positions. Direction of storm motion at landfall was 
determined from figures such as this. 

Any final determination of the track and speed of forward motion of a 
hurricane, especially over data-sparse regions, has inherent uncertainties. The 
track that was finally chosen was based on subjective analysis of all available 
information. Figure A.2 is an example of the information used in our analysis. 



149 



990 4 
30 


kl200 


96* 


\ 1AH . 9Z . 
\ HOUSTON 9_5' M« ^ +3tf 




\ BAYTOWN^Uj ^^___ -^^ 'v*'^^ £" J 




» ELLINGTON AFB--->u-,^-^ U L F ' ^~Jr 

\0600 "S w r J^^ Op >-* 




\ # "^\ >^^ MEXICO 




\ /^^GALVESTON 


+ 


FRECPORT J^""^ +■ 


4- +29' 


-^ 964(»0000CST/I8t» Aw,. 

^S 30 j 


LEGENO 
990 CENTRAL PRESSURE (mb) 
35 RAORJS OF MAX. WNOS <nmi) 
0000 TIME (CST) 




\i800 


+ 


974*1200 
, 14 / I -L +23* 

( 0600 




987$OOOOCST/l 7tn Ay,. 

24 \ 




\^__I800 




"""^»>~ 1200 

998^*^ 
20 >«. 




^^0600 


+ 


. , -f. ^"soooocsi/ieto 

95' 94* 93* !< JP| S, 9' 


96" 



Figure A-l. — Hurricane track for Alicia, 0000 CST August 16 through 1200 CST 
August 18, 1983. 

Hurricane eye positions based on radar observations reported from Galveston, 
Texas, and Lake Charles, Louisiana, are shown as solid dots. Aircraft 
reconnaissance penetration fixes are shown by triangles. Locations of the 
hurricane's center determined from satellite observations are given by 
diamonds. The data from radar fixes and aircraft penetrations were the primary 
sources used in determining the track and speed of the hurricane over the open 
ocean. However, information obtained from satellite observations and from ships 
and oil rigs operating in the area was considered in determining the final track 
and speed of motion. 

A.2.5.2 Forward Speed. The translation speed of the hurricane is an important 
factor in determination of the surge along the open coast and in bays and 
estuaries. Hourly positions were the basic data used to determine the forward 
speed. Speeds between successive hours from positions along the best track were 
first determined and plotted on a time scale and smoothed. Then smooth curves 
drawn from these data were used to adjust the hourly locations. The new 
locations were examined with regard to the observed data and, if necessary, some 
further adjustments were made. This process was continued in an iterative 
fashion until the best combination between smooth forward speeds and observed eye 



150 









<•> £f 



28°N + 
95 °W 



• • •*• 



Q 

LAKE CHARLES 







• • • 



Figure A. 2. — Hurricane eye position obtained froa radar (•), aircraft 
reconnaissance penetration fixes (A), and satellite observations (<i>). 



151 




Figure A.3 • — Minimus pressure recorded at land stations and by 
reconnaissance during Hurricane Alicia (1800 CST August 16 - 
August 18, 1983). 



aircraft 
1200 CST 



positions was obtained. This process helped to obtain the best possible estimate 
of forward speed and hourly locations. 

A.2.5.3 Central Pressure. The most important meteorological input to storm- 
surge models is the intensity of the hurricane which can be parameterized in 
terms of its central pressure. Minimum pressures observed at stations and during 
reconnaissance aircraft penetrations are presented in Figure A.3. These 
observations were not all obtained at the same time. Since the track of the eye 
did not cross any land station location, none of the values reported at land 
stations are equal Co the 'minimum central pressure in the storm. 

Figure A. 4 shows our analysis of pressure data from land stations and aircraft 
reconnaissance flights used to obtain a cime history of Alicia's central 
pressure. A smooth curve was fit to the data by eye. Alicia deepened gradually 



152 




o 


o 


O 


o 


en 


03 


o 


05 


05 



<W 3dflSS3dd !VyiN30 
153 



at an average rate of 1 mb per hour starting from 1200 GMT on August 16 until it 
reached a minimum value almost 2 hours after landfall. A reconnaissance aircraft 
recorded the minimum pressure of 962 mb at 0842 GMT on August 18 (fig. A. 4). We 
consider this pressure to be the lowest that occurred in Hurricane Alicia. The 
short time intervals between central pressures obtained by aircraft, combined 
with other information (cited in sec. A.2.2), did not indicate any lower pressure 
at intermediate times. 

As Alicia continued its north-northwesterly course overland, its intensity 
weakened only gradually over the next several hours. Alicia's central pressure 
reached its minimum and stayed nearly unchanged for another 2 to 3 hours after 
the hurricane center crossed the coast. Hurricane central pressure usually rises 
rapidly after the storm center moves over land. The central pressure of 
Camille (1969), which was a small and intense hurricane, rose at a rate of about 
10 mb per hour for about 5 hours after its center crossed the Mississippi 
coast. For Alicia, the lowest sea-level pressure recorded at Alvin, Texas, was 
967 mb and at Pearland, Texas, it was 972 mb. Alicia weakened rapidly soon after 
it passed the southwestern suburb of Houston, Texas. Its central pressure 
rose to 980 mb as its center passed near Spring, Texas, just 14 nmi west by north 
of Houston Intercontinental Airport (sea-level pressure at Spring reached 982 mb 
at 0952 CST or 1552 GMT - see fig. A.3). 

A.2.5.4 Wind Analysis. In addition to the minimum pressure reported at stations 
during hurricane passage, surface winds were recorded at several weather stations 
operated by the NWS and the military services. The Hurricane Landfall Program 
executed by the HRD of the AOML, NOAA, recorded radar data and collected post- 
storm surface meteorological data from numerous NWS and private sources 
(Powell et al. 1984). This data collection was made available to us for this 
study. We analyzed the windfield for Alicia in two ways. We first examined the 
wind observations of land stations. Next, we did composite streamline analyses 
of the windfields at various intervals near the time of landfall. This wind 
analysis was used to aid in the determination of the radius of maximum winds. It 
also provided some guidance in determining the best track. 

Figure A. 5 shows the time variation of windspeed and sea-level pressure 
recorded at Houston Intercontinental Airport, Texas. The figure shows that the 
maximum wind of 51 kn occurred some 3 hours before the minimum pressure was 
reached at about 1450 GMT on August 18. The maximum wind was observed when the 
hurricane center was about 28 nmi (51.8 km) south of the station. Figure A. 6 
shows similar curves for pressure and windspeed recorded at the EXXON office in 
Baytown, Texas. A maximum wind of 70 kn was observed at 1300 GMT when the storm 
center was 31 nmi (57.4 km) to the west. 

Since surface data were too limited and scattered to analyze the winds when the 
hurricane was located some distance off the coast, all reconnaissance aircraft 
observations within intervals of several hours were combined and plotted. This 
technique, called composite analysis, makes use of the hurricane center as the 
basis of the coordinate system. The position of each observation taken in aerial 
reconnaissance was measured in terms of azimuth angle and radial distance 
relative to the hurricane center at the time of observation. Each wind 
observation was then transposed to the relative location with respect to the 
hurricane center at map time. Figure A. 7 shows a composite analysis based on the 
flight-level wind observations taken from 2040 GMT on the 17th through 0040 GMT 
on the 18th. The transposed observations are shown in this chart. The figure 

154 



60 



I I 1 

HURRICANE ALICIA J 983 



PRESSURE 



PRESSURE AND WIND SPEED 
RECORDED AT HOUSTON (IAH),TX 




06 



i/00 



06 



020 



000 



< 

98o a 



970 



! 2 



18 



9/00 



06 



TIME (GMT) 

Figure A.5. — Hourly observations of sea-level pressure and surface wind speed 
recorded at Houston Intercontinental Airport, Texas, (0600 GMT August 17 - 
0600 GMT August 19, 1983). 

shows an isocach (isolines of constant windspeed) analysis of flight-level 
(1,500 m or 5,000 ft) winds* The isolines are labeled in kn. The analysis is 
assumed to apply to Che center time (2240 GMT) of the composite period. Maximum 
winds of about 85 kn were observed in the front semi-circle at about 15 nmi (2 7.3 
km) from the storm center. 

Powell et aim (1984) constructed composite maps using mean surface and flight- 
level wind data, adjusted to the 10-m level. The observations were plotted at 
transposed locations, relative to the wind center of the storm, as determined 
from aircraft reconnaissance fixes, surface winds, sea-level pressures and radar 
data. Figure A. 8 shows the streamline and isotach analysis of a composite map 
from Powell et al., near the time of landfall (0730 GMT). The analysis assumed 
that the storm structure and intensity had not changed during the period of 
composite, 0400-1100 GMT on August 18. At this time, Alicia exhibited a double 
eye structure. The maximum winds observed during this period in the storm 
(3 9 m/sec or 78 kn) were found in the outer radius by a Coast Guard cutter near 
Galveston, Texas. The extreme winds near the inner core (ayewall) were slightly 
less than those of the outer maximum which was about 30 nmi (55.6 km) from the 
storm center. Analysis of flight-level winds for the same oeriod (diagram not 
shown) revealed maximum flight-level winds of 90-100 kn occurring at about 30 nmi 



155 



50 - 



Q 
UJ 

UJ 

Q. 

W 30 

Q 

Z 



20- 



10 




- 1020 



1010 



HURRICANE ALICIA J 983 
PRESSURE AND WIND RECORDED 
AT BAYTOWN (EXXCN) t TX 
I I I I 



x 

ooo 55 

CO 

UJ 

cc 
a 



990 g 
< 
co 

980 



— 970 



06 12 18 13/00 06 12 13 19/00 06 

TIME (GMT) 
Figure A. 6. — Same as Figure A.5 for Baytown, Texas. 

(55.6 km) to the right of the storm center. This agrees very well with surface 
wind observations. A secondary wind maximum (80-85 kn) , nearer the eye at 
flight-level, was located in the right rear quadrant of the storm. 

A.2.5.5 Radius of Maximum Winds. A common measure of hurricane size is the 
distance between the storm center and the band of highest winds. The determina- 
tion of the radius of the maximum winds was made on the basis of all available 
data for this storm. Three different types of observations were used. The first 
included maximum flight-level winds and estimated surface winds as reported by 
reconnaissance aircraft. The second was the radar-estimated eye wall diameter, 
as well as data on the size of the eye as reported by reconnaissance aircraft and 
by surface stations. Some visual reports were used when the reconnaissance 
aircraft were in the eye of the storm. The third measure, useful only after the 
hurricane was near shore, was the estimated radius deduced from wind records at 
land stations. In Alicia, we relied heavily on the first and the third measures 
to determine the R value. 

Figure A. 9 shows flight-level winds recorded at the 850-mb level between 
13 52-1433 GMT on August 17. The winds were recorded at 1-second intervals by 
reconnaissance aircraft of MOAA's Office of Aircraft Operations and were 
processed and plotted as a function of radial distance from the hurricane 
center. The winds obtained during a traverse of the eye along a path 349° to 
169° revealed that maximum winds of about 45 m/sec (90 kn) occurred near 30 km 



156 




.57 



30°N 



29°N 



28°N 




96°W 



95°W 



94°W 



Figure A. 3. — Streamline (solid lines) and 10-m isotach (dashed lines) analysis 
for Hurricane Alicia, 0730 OCT August 18, 1983 (from Powell et al. 1984). 

(16 nmi) from the storm's center. Similar radial wind profiles constructed from 
winds recorded in each traverse of the hurricane eye were plotted bv computer and 
made available to us by the HRD/AOML, NOAA. Examining a series of wind profiles, 
we obtained estimates of R at various times. Further analysis of composite 
charts of flight-level winds, previously discussed, provided additional insight 
into the time history of R in Alicia. 

Figure A. 10 shows the radial distance of wind maxima, thus obtained, at various 
times between 0600 GMT on August 17 and 0000 GMT on the 19th. Smooth lines drawn 
through these data points provided us with curves from which the radius of 
maximum winds was determined. Radial distances of maximum winds obtained from 
analysis of flight-level winds are shown by solid boxes; those deduced from 
surface winds recorded at land stations are given by triangles. The magnitude of 
extreme winds recorded at a given time was classified into two categories, a 
primary and a secondary wind maximum. The primary wind maximum is denoted by a 
solid line, while the secondary wind maximum is indicated by a dashed line. A 
shift of the primary wind maximum from a radial distance of about 15 nmi 
(2 7.8 km) to about 30 nmi (55.6 km) from the center seems to have occurred around 
0600 GMT on August 18. 



158 




Nl u > 



/-j 



M/'- 



90 



30 



50 30 10 -10 -30 

STORM DISTANCE (km) 
Figure A.. 9. — Flight-level (1500 a) vind3 recorded along radials through the 
center of Hurricane Alicia, 1352-1433 GMT August 17, 1983. 



A«2 .6 Discussion 

The value of R is one of the important factors Co be prescribed in a numerical 
computation of hurricane surges at the coast as well as in bays and estuaries. 
The R value, together with a precisely determined storm track specify the 
location of maximum winds along the coast. This, in turn, influences the water 
level produced by surface wind stress in a storm-surge model. It is important 
for surge modelers, as well as users of hurricane surge models, to have precise 
meteorological information in order to calibrate or verify a numerical surge 
model. The radius of maximum winds for Alicia shifted from 15 nmi (2 7.8 km) to 
3 nmi (58.6 km) near the time of landfall. The transformation of storm size for 
Alicia took several hours to complete. The high winds near the inner core caused 
severe damages to downtown Houston, Texas. However, high-water levels in 

Galveston 3ay (close to 11 ft above MSL at Baytown, Texas) were generated by the 
winds within the region of highest winds. After examining all available data, we 
concluded that R for Alicia shifted from 15 nmi (27.8 km) to 30 nmi (55.6 km) 
just before the hurricane made landfall and that the larger R should be applied 
to surge computations for the Galveston Bay area. 

Hurricane data of recent years have shown large variabilities in hurricane 
parameters at various stages of a hurricane's life cycle. After a hurricane 
moves over land, its characteristics often change abruptly, due to larger surface 
friction and modifications to the heat and energy supply. Such changes in the 
characteristics of the hurricane would result in a departure from the 
standardized wind profile of the storm-surge model. Hurricane parameters, 
especially the index R, given in Tables 1 through 3 may not be the best values 



159 



2 

X 40 

O 



1 1 1 

RADIAL DISTANCE OF WIND MAXIMA 
HURRICANE ALICIA, AUGUST I 983 



- RECON. DATA 
7 LAND STATIONS 



TIME (GMT) 

Figure A. 10. — Radius of primary (solid line) and secondary (dashed line) wind 
maxima in Hurricane Alicia, August 17-18, 1983. 

for replicating observed surges with a standardized wind profile. The variation 
in R near landfall might have to be examined on a case-by-case basis before a 
suitable value can be determined for the calibration of a numerical surge 
model. In the calibration process, the computed model winds, in addition to the 
computed high-water level, should be verified using observed data to ensure the 
adequacy of the wind model used in the numerical surge computation. 

A.3 Hurricane David, September 2-5, 1979 

A.3.1 Introduction 

Hurricane David emerged from the central Caribbean on September 2 after 
devastating the Dominican Republic and rapidly weakening to tropical storm 
strength over the mountains of Hispanola. David was the strongest hurricane to 
hit Santo Domingo, Dominican Republic since 1930 (Hebert 1980). Once over water 
north of Cuba, David began to reintensify as it moved northwestward and 
approached Andros Island in the western Bahamas with winds of 61-69 kn 
(DeAngelis 1979). As the center crossed the island late in the afternoon on 
September 2, it appeared to be heading toward the Miami area (fig. A. 11). A turn 
to the north-northwest, however, brought the slowly strengthening hurricane about 
50 nrai (92.6 km) east of Miami on Labor Day, September 3. Winds of 50 kn were 
reported buffeting Miami 3each by 0800 GMT September 3. David continued moving 
north-northwestward and passed within 2 5 nmi (46.3) of West Palm 3each with a 
minimum central pressure of 973 mb at 1445 GMT September 3. Winds of 50 kn were 
experienced at West Palm Beach shortly before David's nearest approach. At 
1730 GMT on September 3, the storm center made landfall just south of 
Stuart, Florida, with a central pressure of 968 mb. Winds of 60 kn were recorded 



160 




Figure A.ll. — Track with central pressures (mb) for Hurricane David, 
September 2-5, 1979. 



161 



Table A.l. — Time, flight pattern, and flight level of NOAA/RFC missions into 
Hurricane David, September 1979 



Mission 



Time period 
(GMT) 



Pattern 



Flight level(s) 
(ft) 



790902F 

7909021 

7 90902H 



02/0145-092 5 

02/1130-1853 
02/2002-03/0454 



east-west 
race track 



star 
Recon. 



5,000 

variable 

variable 



790903F 
7909031 



03/0504-1240 star (see fig. A. 12) 5,000 

03/2312-04/0641 along FL coast variable 



790904H 



04/1723-05/0128 



modified star 

(eye partly onshore) 



variable 



The missions are designated by an identification code, YYMODAAC where: 

YY = year (F = NOAA/RFC C130B aircraft 41 

MO = month AC = aircraft (H = NOAA/RFC WP-3D aircraft 42 

DA = day of the month (i = NOAA/RFC WP-3D aircraft 43 



at Stuart at 1600 GMT. David remained close to the Florida east coast for the 
next 11 hours as it moved north-northwestward over land. By 0600 GMT 
September 4, the storm center had moved back over open water north of Cape 
Canaveral. David was the first hurricane to strike the Cape Canaveral area since 
192 6 (Hebert 1980). Central pressures in David remained steady as it made its 
way north toward Georgia. Landfall occurred for a second time in the United 
States at 1822 GMT September 4 north of Brunswick, Georgia, with a minimum 
central pressure of 968 mb. David continued on a northerly track and passed just 
west of Savannah, Georgia, at 2346 GMT September 4. 

A .3 .2 Previous Studies 

Hebert (1980) prepared a detailed description of Hurricane David and included 
meteorological data from land stations as far south as the Lesser Antilles, and 
as far north as Mt. Washington, New Hampshire. He compiled meteorological data 
from regularly reporting stations, as well as various unofficial sources which 
were used in the analysis of the variation of central pressure with time (shown 
in fig. A. 15). The National Hurricane Center published an annual verification and 
data tabulation for Atlantic tropical cyclones of 1979 which included Hurricane 
David (Hebert and Staff 1980). The compiled data tabulations give David's 
center-fix positions obtained by aerial reconnaissance penetrations, satellite 
images, and land-based radar. Central pressures, maximum winds and other data 
observed by aerial reconnaissance were also included for Hurricane David. 



162 



DIRECTION OF STORM MOVEMENT 




Optiona 



80 NM leg 



Figure A. 12. — Reconnaissance flight pattern, designated as star pattern, 
Hurricanes David and Allen (refer to Friedman et al. 1982). 



used in 



Howell at al. (1982) provided a report of tide data during; the passage of 
Hurricane David at Miami Beach, Palm Beach, and Vero Beach, Florida. Storm 
surges at Palm Beach and Vero Beach were computed by Howell et al. using a 
numerical storm-surge model and compared with observed values. 

A.3.3 Aircraft Data 

NOAA research aircraft flew six missions into Hurricane David during the period 
September 2-5. Table A.l summarizes the flight patterns, flight levels and the 
time periods for which meteorological and flight data were recorded. The flight 
patterns flown in these missions included a 'star' type (fig. A. 12) and a 'Recon' 
type. The 'Racon' flight pattern was a deviation from typical flight patterns. 
In this case, the actual pattern completed was designed to optimize both the 
determination of the storm center location and collection of research data. A 



163 



detailed inventory of airborne research meteorological data is described by 
Friedman et al. (1982). This set of NOAA flight data was supplemented by Air 
Force reconnaissance flight data recorded on the morning of September 4. 

A.3 .4 Central Pressure 

A.3 .4.1 P From Aerial Reconnaissance. Minimum central pressures were recorded 
nearly continuously from September 2-4 by NOAA and Air Force reconnaissance air- 
craft when Hurricane David was moving over open water. Pressure values were 
obtained from Hebert et al. (1980). These pressure values were used in 
Figure A. 15. When Hurricane David moved over land, reconnaissance aircraft did 
not penetrate the eye to obtain a pressure reading because of increased 
turbulence over land. 

A.3 .4.2 P Q From Land Station Observations. Once Hurricane David was over land, 
station reports of hourly weather observations and barograph traces were used to 
determine minimum pressures. If the center of the hurricane eye passed directly 
over a land station, then the minimum pressure could be readily determined. 
Hurricane David, however, did not pass directly over any land stations. Since 
several stations were very close to the track, their minimum pressures were used 
to estimate the storm's minimum pressure. Figure A. 13a shows the time variation 
of minimum pressures recorded at Shuttle Airport, Florida every 3 hours. From 
this plot, the lowest pressure observed during the passage of David, 974 mb, 
occurred at about 0300 GMT September 4, when the storm's eye was located only 
about 5 nmi (9.3 km) to the west of the station. This estimate was plotted in 
Figure A. 15. Another example of (hourly) station pressure data is shown in 
Figure A. 13b for Savannah Municipal Airport, Georgia. A minimum pressure of 
970 mb was experienced at 2300 GMT September 4 when David was about 7 nmi (13 km) 
to the west. This estimate was also used in the analysis shown in Figure A. 15. 

A.3 .4.3 Pressure Fit at the Coast. Minimum pressures determined at the Florida 
and Georgia coasts were not based on any single source. Observed pressures were 
extrapolated inward to P using visually-fitted radial pressure profiles based on 
equation 1. Figure A. 14a shows a subjectively fit pressure profile curve at the 
Florida coast, near the time of landfall, at 2100 GMT September 3. Pressure 
observations from several land stations were plotted against distance from storm 
center at 2100 GMT. Then a curve was drawn to fit the data. Figure A. 14b is 
another example of the pressure profile curve except at 1800 GMT September 4, at 
the Georgia coast. In both cases, a minimum central pressure of 968 mb was 
estimated. In the case of the Georgia coast, a NOAA research aircraft measured a 
minimum 700 mb height of 2 82 m at 1822 GMT September 4. Using a nomogram for 
estimating surface pressure in the eye of tropical cyclones (Jordan 1957), a 
central pressure of 968 mb was also estimated. 

A.3 .4.4 Time Variation of P . Hurricane David was most intense (central 
pressure of 92 4 mb) while still located in the Caribbean Sea, south of Puerto 
Rico. The analysis for this period was used in Chapter 4. As David emerged from 
the central Caribbean Sea, however, central pressures moderated considerably (see 
fig. A.ll). Figure A. 15 shows the time variation of central pressure in David 
for the period of September 3-5. Minimum pressures recorded by reconnaissance 
aircraft and land stations at various times were used to obtain a time history of 
David's central pressure. The line drawn is a curve fit to the data by eye. 



164 





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Figure A. 13. — Sea-level pressure observed during passage of hurricane David 
(September 1979) at (a) Shuttle Airport, Florida, and (b) Savannah (Municipal 
Airport) , Georgia. 



165 




250 300 350 

DISTANCE FROM STORM CENTER C rani) 




100 150 200 250 300 350 400 

DISTANCE FROM STORM CENTER Cnmi) 

Figure A. 14. — Pressure—profile curve during Hurricane David for (a) Florida coast 
at 2100 GMT, September 3, 1979, (b) Georgia coast at 1800 GMT, September 4, 
1979. 



166 



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STORM DISTANCE (km) 

Figure A.16. — Flight-level ri?As recorded along radlals through the center of 
Hurricane David, (a) 2308-2356 QfT, September 2 , (b) 0644-0748 GHT, 

September 3, and (c) 1751-1341 GMT, September 4, 1979. 

Reconnaissance aircraft reported a minimum pressure of 96 5 mb at 0051 GMT 
September 3 just as David crossed Andros Island, about 120 nmi (222 km) southeast 
of Miami, Florida. A central pressure of 966 mb was recorded by aerial 

reconnaissance at 0302 GMT. By 0531 GMT September 3, another mission reported a 
central pressure of 981 mb. The pressure difference in these 2 .5 hours was 
15 mb. This large pressure rise seems to be inconsistent with Che other data as 
Figure A. 15 shows and no explanation can be given. Hurricane David approached 
the southeast coast of Florida at a speed of about 10 kn, and a central pressure 
of 968 mb was determined at landfall at about 1730 GMT September 3. This value 
is the pressure recorded in Table 2. As David moved northwestward over land 
along the Florida coast (fig. A.ll), central pressures increased very gradually 
until the storm exited the coast and moved over water again. A central pressure 
of 975 mb was consistently reported by Air Force reconnaissance aircraft from 
1142-1515 GMT September 4. During this time, David was moving over water north 
of Cape Canaveral at about 12 kn. As the hurricane approached the Georgia coast, 
pressures dropped at about 2 mb/hr from 1515 GMT until a low pressure of 968 mb 
was determined at landfall (see sec. A.3.4.3), about 1822 GMT September 4. David 
moved inland at about 10 kn and weakened slowly. Savannah, Georgia experienced a 
minimum pressure of 970 mb when the center of David was only about 7 nmi (13 km) 
to the west and 40 nmi (74 km) inland. 



169 



A*3 .5 Radius of Maximum Winds 

A.3.5.1 R From Aerial Reconnaissance. Figure A. 16a shows a wind profile 
constructed from flight-level wind data recorded between 2 308-2 3 56 GMT 
September 2. The winds were recorded during a north-south traverse through the 
eye and are plotted against radial distance from the storm center. The figure 
indicates that a wind maximum is located to the north of the center at a radial 
distance of about 35 km (18.9 nmi). This value was plotted in Figure A. 18 at 
2332 GMT September 2. Figure A. 16b is another wind profile for Hurricane David 
constructed from flight-level winds recorded between 0644-0748 GMT September 3 . 
At this time, the storm center was located over open water about 68 nmi (12 6 km) 
east-southeast of Miami, Florida (see fig. A.ll). Flight-level winds were 

recorded during a northeast-southwest traverse through the eye. The wind profile 
indicates that maximum winds occurred at a radial distance of about 45 km 
(24 nmi) northeast of center. This value was plotted in Figure A. 18 at 0716 GMT 
September 3. Figure A. 16c shows another wind profile constructed from data 
recorded between 1750-1841 GMT September 4. At this time, the storm center was 
over water north of Cape Canaveral and approaching landfall on the Georgia 
coast. The winds were recorded during an east-west traverse through David's 
eye. Figure A. 16c indicates a maximum wind at a radial distance of about 20 km 
(10.8 nmi) west of center. This value is plotted at about 1815 GMT September 4 
in Figure A. 18. Figures A. 16a through A. 16c suggest the existence of secondary 
maxima (indicated by solid dots in fig. A. 18) which were relatively short- 
lived. Analysis of composite maps (diagrams not shown) revealed that these 
secondary maxima were scattered and quite disorganized. They were not considered 
relevant in the specification of the parameters that are the focus of this study. 

A.3.5.2 R From Land Station Observations. Once the storm moved inland, land 
stations were the primary source of data. Data from these stations were obtained 
from the NCDC in Asheville, North Carolina, where all raw data from station 
observations are stored. 

Figure A. 17a shows a time variation of windspeed and wind direction for Shuttle 
Airport, Florida from 1200 GMT September 2, to 0000 GMT September 5. This plot 
consists of hourly wind observations as Hurricane David passed just west of the 
station (0300-0400 GMT September 4). Note the shift in wind direction as the 
storm center passed. Winds veered from the east to east-southeast then south 
indicating the path of the storm center was to the west of the station. A 
maximum wind of about 3 7-3 8 kn (19-2 m/s) was experienced at Shuttle Airport at 
053 GMT September 4 when the storm center was located approximately 2 nmi 
(3 7 km) away from Shuttle Airport (see hurricane track on Fig. A.ll). 
Figure A. 17a also shows the distance of the storm from Shuttle Airport (dashed 
line). Using this information, a radial distance of 2 nmi (3 7 km) was 

determined for the wind maxima and was plotted in Figure A. 18 at 0530 GMT 
September 4. Figure A. 17b shows another plot of hourly windspeed and direction 
against time for Savannah Municipal Airport, Georgia from 0600 GMT September 3 to 
1700 GMT September 5. The wind direction at Savannah as David's center passed 
nearby shifted from the east to east-southeast then south and finally 
south-southwest. This indicates that the hurricane passed to the west of the 
station (fig. A.ll). A maximum wind of about 37 kn (19 m/s) occurred at Savannah 
at 2230 GMT September 4. The track in figure A.ll indicates that the hurricane 
center was only about 10 nmi (18.5 km) away from Savannah at 2230 GMT 
September 4. 



170 



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173 



A.3.5.3 Time Variation of R- Figure A. 18 shows the time variation of the radius 
of maximum winds in Hurricane David from 0300 GMT September 2 to about 0800 GMT 
September 5. Radial distances of maximum winds from the storm center measured by 
reconnaissance aircraft at various times, and those obtained from analyses of 
land-station wind records were used to obtain this time history. 
Reconnaissance aircraft reported the majority of maximum winds needed for 
R-value analyses, especially before 1200 GMT September 3. The line shown was 
drawn to the data by eye. 

As Figure A. 18 shows, the radius varied from about 17 to about 28 nmi 
(31.5-51.9 km) between 2100 GMT September 2 and 1200 GMT September 3. By 
1400 GMT September 3, land stations were beginning to experience maximum winds. 
West Palm Beach, Florida experienced maximum winds when the hurricane center was 
about 18 nmi from the station. Stuart, Florida recorded maximum winds at about 
1600 GMT September 3 or 1.5 hours before the storm center made landfall in 
Florida. The radius of maximum winds remained steady at 2 6 nmi (48.1 km) during 
landfall. By 2100 GMT September 3, the radius began decreasing again until about 
0100 GMT September 4 when a reconnaissance aircraft reported maximum winds at a 
radius of 20 nmi (37 km). The radius remained steady once again at 20 nmi 
(3 7 km) as the storm moved out over water north of Cape Canaveral (see 
fig. A.ll). Both Melbourne and Shuttle Airport, Florida, experienced maximum 
winds when David was located 20 nmi (37 km) from the station before exiting the 
coast. From about 1030 GMT September 4 until landfall in Georgia at 1822 GMT, 
the radius of maximum winds decreased to 10 nmi (18.5 km), as determined from 
maximum winds recorded by a reconnaissance aircraft at about 2000 GMT. This was 
the smallest radial distance reported within 150 nmi (2 78 km) of the east 
coast. Hunter AFB and Savannah, Georgia, both recorded maximum winds soon after 
the storm center made landfall when David was located 10 nmi (18.5 km) to the 
south. After passing Savannah, Georgia, the radius of maximum winds expanded 
rapidly. Columbia, South Carolina, experienced maximum winds when the storm was 
located at a distance of about 47 nmi (87 km) from the station at 0600 GMT 
September 5. 

Because of the abrupt change in storm size after making landfall, using an 
R value of 10 nmi (18.5 km) in a numerical surge computation could not replicate 
surge heights along the coast produced by Hurricane David (Jarvinen 1985, private 
communication). As David moved parallel to the coast and passed some 40 nmi 
(74 km) inland of Charleston, South Carolina, its track and R influenced the 
position of the band of strongest winds along the coast. This factor, in turn, 
affected the coastal surges and the maximum wind setup effects in Charleston 
Harbor. In replicating high water levels experienced in Charleston, either 
varying R with time or using a large R value in a numerical surge computation 
would be required in order to obtain realistic results. 

A.4 Hurricane Allen, August 2-10, 1980 

A. 4.1 Introduction 

Hurricane Allen originated near the Cape Verde Islands, off the west coast of 
Africa, and developed into the second most severe Atlantic hurricane in modern 
records. It reached tropical storm strength in the early hours of 
August 2, 1980, and attained hurricane strength that evening (see fig. A. 19). 
Its central pressure dropped to 951 mb by the evening of the 3rd as the eye 
passed just north of Barbados and south of St. Lucia. The hurricane continued 
westward into the Caribbean at about 2 kn and passed south of Puerto Rico during 

174 




175 



the evening of the 4th. Its central pressure deepened and reached 911 mb, the 
lowest pressure ever recorded in the eastern Caribbean, on the early morning of 

the 5th. 

The hurricane weakened as it passed the southwest tip of Haiti and moved 
between Jamaica and Cuba. This was the first of three strengthening-weakening 
cycles in Allen's life history that are unprecedented in hurricane records. 
Allen reintensified rapidly as the circulation moved over the northwestern 
Caribbean Sea. Arriving at Yucatan Channel on the 7th, its central pressure 
deepened to 899 mb, the lowest pressure ever observed in the western Caribbean 
and the second lowest ever recorded for an Atlantic storm. The hurricane 
weakened for the second time when it moved past the north coast of the Yucatan 
peninsula. Its central pressure rose rapidly, reaching 961 mb on the morning of 
the 8th. As the hurricane continued west-northwestward across the warm open 
water of the Gulf of Mexico, Allen deepened once again with a minimum pressure of 
909 mb observed during the night of the 8th. 

As the hurricane approached the Texas coast on the 9th, its intensity weakened 
and the forward speed decreased. Allen held to its west-northwesterly course 
until mid-day and then turned northwestward. After crossing the southern end of 
Padre Island just northeast of Brownsville, Texas, Allen continued in a 
northwesterly direction. By early morning of the 10th, Allen moved inland at a 
slightly faster speed and turned gradually towards the west-northwest. In 
addition to the damage from the hurricane winds and storm surge, Hurricane Allen 
also spawned at least a dozen tornadoes over Texas. 

A.4.2 Previous Reports 

The National Hurricane Center provided a description of significant features of 
all Atlantic tropical storms that occurred during 1980, including Hurricane 
Allen. This information was published in the Monthly Weather Review (Lawrence 
and Pellissier 1981) and in the National Summary of Climatic Data (National 
Hurricane Center 1980). Significant features mentioned in regard to Allen were 
the minimum central pressure of record, the rapid deepening, and the fluctuations 
in intensity during its life cycle. The appearance of a double eye configuration 
was noted in a Brownsville radar picture taken when Allen was 100 nmi (185 km) 
off the coast. 

Willoughby et al. (1982) described secondary wind maxima associated with 
concentric eye walls and the evolution of the hurricane vortex in Allen and a few 
other hurricanes. They described the sequence of events as reported near Allen's 
inner core by reconnaissance aircraft on August 5 and 8, 1980. Based on data 
collected in Allen and other hurricanes, they concluded that an outer maximum is 
frequently observed to constrict about a pre-existing eye and replace it and the 
central pressure tends to decrease during the constriction. They suggest that 
the concentric eye phenomenon is most frequently observed in intense, highly 
symmetric systems. 

The NHC publication on annual data and verification tabulation for the 1980 
Atlantic tropical cyclones (Taylor and Staff 1981) also includes a list of 
Allen's center fix positions obtained by aerial reconnaissance penetrations, 
satellite images, and land-based radar. The hurricane's central pressure, 
maximum winds, and other data observed by reconnaissance aircraft are also 
included in that report. 

176 



Ho and Miller (1983) analyzed available meteorological data for Hurricane Allen 
during the period surrounding landfall to provide information for use in dynamic 
storm surge models. Detailed analyses were made of the storm track, forward 
speed, central pressure, and radius of maximum winds. 

Marks (1985) studied the evolution of the structure of precipitation in 
Hurricane Allen. He used reflectivity data from airborne radar systems on board 
the three NOAA aircraft to specify the horizontal and vertical precipitation 
distributions within 111 km (60 nmi) of the hurricane center. He found that the 
most striking changes in structure during the 6-day period were the rapid con- 
traction in eyewall radius and the development of a secondary ring of intense 
reflectivity 80-100 km (43-54 nmi) from the storm center. He further stated that 
these changes in eye radius appeared to be related to the vortex evolution, as 
discussed by Willoughby et al. 

A.4.3 Reconnaissance Flight Data 

NOAA/RFC research aircraft flew 12 missions into Allen during the 6 day period, 
from August 5-10. Table A. 2 lists the flight patterns, flight levels and the 
time periods for which meteorological and flight data were recorded in each of 
the 12 missions. The table lists two 3-aircraft missions flown on August 5 and 
August 8 and single-aircraft missions on other days. Willoughby et al. (1982) 
compared the calculated and observed properties of Hurricane Allen on August 8 
for all three different flight levels (500-, 600-, and 850-mb levels). He 
concluded that one can obtain reliable indications of the evolution of the 
symmetric vortex from any lower tropospheric flight level above the boundary 
layer. 

A.4.4 Central Pressure Analysis 

Figure A.2 1 shows our analysis of the pressure information from reconnaissance 
aircraft that was used to obtain a time history of Allen's central pressure. 
This figure clearly shows the three strengthening-weakening cycles. Allen 
reached a record low pressure (for specific areas) at each of its deepening 
stages. A minimum pressure of 899 mb observed at 1742 GMT on August 7 was the 
lowest observed in Hurricane Allen. The central pressure was only 7 mb higher 
than the record pressure of 892mb observed in the Labor Day, 193 5 storm that 
struck the Florida Keys. The low pressure of 909 mb, observed at 0558 GMT on 
August 9, was considered to be the lowest that occurred in Hurricane Allen as it 
approached the coast. The short time interval between central pressures obtained 
by aircraft, combined with other information, did not indicate any lower pressure 
at intermediate times. As Allen continued its course west-northwestward, 
approaching the Texas coast, its intensity weakened. While the hurricane's 
central pressure rose steadily, the characteristics of its inner core appeared to 
have undergone dramatic changes, as discussed in the next section. 

A.4.5 Wind Analysis 

Flight-level winds on each traverse were plotted by computer and made available 
to us by the Hurricane Research Division of NOAA/AOML. The aircraft locations 
for observation of flight-level winds were translated to positions relative to 
the storm center. From these records, composite maps of winds at given intervals 
were constructed. Another source of information came from Air Force 
reconnaissance aircraft that flew into the hurricane. 



177 



Table A.2. — Time, flight pattern, and flight level of NOAA/RFC missions into 
Hurricane Allen, August 1980 



Mission Time period 
(GMT) 



Pattern(s) 



Flight level(s) 
(ft) 



800805F 
800805H 

8008051 
800806H 

80080 61 
800807H 
800808F 
800808H 
8008081 
8008091 
800809H 

80081 OF 



05/1028-1742 
05/102 1-1933 



05/1015- 
06/1239- 
06/1825- 
07/1601- 
08/162 0- 
08/1631- 
08/1617- 
09/162 5- 
09/2324- 
10/1006- 



■1932 

-1910 

•07/0031 

•08/0017 

•09/0059 

■09/0107 

•09/0110 

•10/02 10 

•10/0947 

•1630 



figs. A.2 0a, A.2 0b 

fig. A.20a 

fig. A.2 0b 

fig. A.20a, A.20b 

fig. A. 12 

fig. A.20a (modified) 

fig. A.2 0a (modified) 



cross 

along coast 

2 5 nmi off coast 



10,000 

variable 
variable 

1,500, 5,000 

1,500, 10,000 (last half) 

5,000 

variable 

12 ,000 

18,000, 20,000 

5,000 

10,000 

variable 

700- and 850-mb levels 



'The missions are designated 
YY = vear 
MO = month 
DA = dav of the month 



by an identification code, YYMODAAC where: 

F = NOAA/RFC C130B aircraft 41 

<fH = NOAA/RFC WP-3D aircraft 42 

I = NOAA/RFC WP-3D aircraft 43 



Figure A.22 is an example of flight-level windspeeds plotted against radial 
distances from the storm center. The wind data were recorded in a 3 12° to 132° 
traverse through the eye between 153 5 and 1627 GMT on August 5. The maximum 
winds can be located at radial distances of 15 and 19 nmi (27.8 and 35.2 km). A 
secondary maximum appeared near radial distances of 50-60 nmi (82.6-111 km) at 
the rear quadrant of the storm. At this time, Allen's central pressure had risen 
to 93 7 mb, after having reached a minimum of 911 mb at 0000 GMT on the 5th 
(fig. A.2 5). Figure A. 23 is another example of flight-level windspeed plotted 
against radial distances from the storm center. This plot shows wind data 
observed between 1844 and 1945 GMT on August 7. The maximum winds recorded 
during this north to south traverse through the storm center were located at 
radial distances of 5 and 10 nmi (9.3 and 18.5 km). The maximum winds decreased 
rather rapidly with increasing distance away from the center. Allen, at this 
time, was a small and extremely intense hurricane, having reached its minimum 
pressure of 899 mb less than 2 hours earlier (see fig. A.2 1). Figure A.24 is an 



178 




(b) 



DIRECTION OF STORM MOVEMENT 
1 




~50nmi 



v^^ ~i5nmi 



Figure A-20, — Reconnaissance flight patterns used in Hurricane Allen (refer Co 
Friedman et al. 1982). 



179 





7/00 06 



8/00 06 12 18 9/00 06 12 18 10/00 06 12 
TIME (GMT) 



Figure A-2 1. —Central pressure (sea level) for Hurricane Allen, 
3-7, and (b) August 7-10, 1980. 



(a) August 



example of flight-level windspeed plotted at translated positions relative to Che 
storm center. The wind data were observed between 02 00 and 0400 GMT on August 9 
during the third deepening cycle within Allen's life span. The wind distribution 
indicates that maximum winds occurred at radial distances of 11 nmi (20.4 km) and 
about 54 ami (100 km) from Che center. Similar distributions of flight-level 
winds can be identified in composiCe maps of other time periods (diagrams not 
shown) as Allen approached Che Texas coast. The evolution of Che wind 

distribution in Allen during this period, shifting from a small size hurricane Co 
one with R of about 40 nmi (74 km), was described by Ho and Miller (1983). 



180 




50 10 -30 

STORM DISTANCE (km) 



Figure A-22. — Flight-level winds recorded along radials through the 
Hurricane Allen, 1535-1627 GMT, August 5, 1980. 



center of 



9C 


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Figure A .23. — Flight-level winds recorded along radials through the 
Hurricane Allen, 1844-1945 GMT, August 7, 1980. 



center of 



181 




30 



30 60 90 
DISTANCE (km) 



Figure A.2 4. — Composite map of flight-level winds (m/sec) recorded between 0200 
and 0400 GMT, August 9, 1980. 

A.4.6 Time Variation of Central Pressure and Radius of Maximum Winds 

Figure A.2 5 shows the time history of central pressure for Allen (from 
fig. A.2 1) together with radial distances of observed maximum winds recorded at 
each traverse of the hurricane center. Analysis of these radial distances 
yielded the variation with time of the radius of maximum winds. Generally 
speaking, Allen was a small hurricane except for the period when it approached 
the Texas coast and moved over land. Prior to this period (9 hr before landfall) 
the time variation of maximum winds indicated that the radial distances of wind 
maxima increased to 2 0-2 5 nmi (3 7-46.3 km) during Allen's two weakening stages. 
However, radial distances of wind maxima stayed within 4 to 15 nmi (7.4-2 7.8 km) 
of the center when Allen's central pressure dropped below 93 mb in each of the 
three deepening stages. The fact that Allen's minimum pressure in each of the 
three deepening cycles occurred some distance from land, does not exclude the 
possibility that a hurricane could attain its maximum intensity (or minimum 
central pressure) at or near the time of landfall. Hurricane Camilla (1969) is 
an example of a hurricane which maintained its intensity of about 90 5 mb for some 
3 6 hours before it crossed the Mississippi coast. 

A#4.7 Relation of ? and R in Hurricane Allen 

Figure A.2 6 is a plot of central pressure versus radial distance of maximum 
winds recorded by aircraft reconnaissance during the oeriod August 3 through 
August 9. Data points used in the plot included those instances when both wind 



182 



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5 10 ^ 15 20 

RAOIAL DISTANCE (nmi) 



Figure A.2 6. — Concurrent observations of central pressure and radius of maximum 
winds for Hurricane Allen, August 3-9, 1980. 

and pressure data were recorded in a traverse of the hurricane center. Some of 

the data points (with no concurrent observations of P and R) shown in previous 

diagrams were not included in this plot. During the period of observation 

(August 3-9), Allen traveled from the Caribbean through the Yucatan Channel into 

the Gulf of Mexico. It covered a distance of about 2 ,000 nmi (3704 km) from 

latitude 14°N through 27°N. Except for a few instances of larse R observed in 

the weakening stages, Allen's maximum winds stayed within 15 nmi (27.8 km) of the 

center. Allen was essentially characterized by small R's before it reached the 

Texas coast. However, the R values in Allen, as well as in other intense 

Atlantic hurricanes, tend to be small and a non-linear relation may exist between 

P and R. 
o 



184 



APPENDIX B 

Statistical Methods for Tests of Homogeneity and Independence 

B.l Introduction 

The statistical methods used in this report to test the homogeneity of 
hurricane parameters and interrelations between them are discussed in this 
appendix. The methods used to test for homogeneity include cluster analysis, 
discriminant analysis, principal component analysis, and the Mann-Whitney test; 
those for the test of independence include the Spearman test and contingency 
table analysis using the Chi-square test. 

For these methods, this appendix describes assumptions, and where appropriate, 
the null hypotheses, the confidence levels, and decision rules. We also briefly 
discuss the rationale for choosing a method, its limitations, and the guidelines 
for interpreting the test results. 

B.2 Methods for the Test of Homogeneity 

Among the methods for the test of homogeneity, cluster analysis, discriminant 
analysis and principal component analysis each consider several parameters, 
whereas the Mann-Whitney test is based on only a single parameter. 

B«2.1 Cluster Analysis 

B.2. 1.1 Description of the Method. In cluster analysis, objects are assigned to 
groups or clusters suggested by the data sample, not by any grouping defined a 
priori. In this study, a hurricane was considered an object for the purpose of 
statistical analysis. That is, all parameters associated with a given storm were 
used to characterize the hurricane. There are many clustering methods (e.g., SAS 
1982); we chose the centroid method for this study. 

The actual computation was performed using the CLUSTER procedure in the SAS 
system. The procedure computes the Euclidean distances between objects and 
assigns those objects that are close to each other to the same cluster. In this 
study, the Euclidean distance was computed using coordinates represented by P , 
R, 9, T, m, (b and A. In the centroid method, the distance between two clusters 
is defined as the Euclidean distance between their centroids (vector means). 

The procedure provided a cluster hierarchy from level one to level N, where N 
is the number of objects in the data sample. In this study, N is the number of 
hurricanes; if any hurricane parameter was missing, that hurricane was omitted. 
In the cluster hierarchy, there is only one cluster at level one and there are N 
clusters at level N. The cluster at level one contains all the objects in the 
data sample, and every cluster at level N contains only one object. As shown in 
Figure B.l, every cluster at a given level is completely contained in a cluster 
at the preceding level. For example, a cluster at level four may contain 



Mention of a particular commercial product should not be considered an 
endorsement by the federal government. 

185 



MILEPOST 


NUMBER OF CLUSTERS 


RANGE 


2 


3 


4 


5 


6 


7 


8 


9 


11-243 


© 





© 


© 


© 


© 


© 


© 


296-500 


o 


© 


560-671 


© 


© 


© 


© 


© 
© 


718-904 


966-1201 


© 


© 


© 


© 


1292-1584 


© 


© 


© 


© 


© 


© 


© 


© 


1752-1945 


© 


© 


© 


© 


© 


© 


© 


2043-2294 


© 


© 


© 


2532-2750 


© 


© 


© 


© 


© 


© 



Figure B.l. — Levels two through nine of the hierarchical clusters of landf ailing 
hurricanes, based on parameters P , R, 9, T, m, d> and \ . The circled numbers 
are the cluster identification numbers. 

exactly the same objects of one cluster at level five (cluster 2 in fig. B.l), or 
it may' contain exactly the same objects of two clusters at level five (cluster 1 
at level 4, and clusters 1 and 4 at level 5 in fig. B.l). The user must 
determine the most appropriate number of clusters. When the number of clusters 
is chosen, the parent cluster of each object (hurricane) can be identified using 
the TREE procedure of the SAS system. 

B.2.1.2 Rationale for Choice. Some clustering methods recuire that the sample 
data be normally discributed. The hurricane data sample has large natural 
variability, and' the normality of our data could not be reliably tested. We 
chose to use the SAS CLUSTER Drocedure since it did not reauire that the data 
sample be normal. 



186 



B.2.1.3 Limitations of the Method. No satisfactory method has heen developed to 
determine the appropriate number of clusters. This is dependent on the data 
sample and nature of the phenomena being considered. 

B.2.1.4 Interpretation of the Results. Conclusions drawn from cluster analysis 
are dependent on the selection of the number of clusters and must be interpreted 
cautiously. Scatter diagrams of the original parameters were helpful for the 
determination of the optimum number of clusters. Other methods, both 
nonstatistical and statistical, were also considered to help interpret the 
results of cluster analysis. In this study, we relied heavily on meteorological 
judgment; in addition we used discriminant analysis and principal component 
analysis to help evaluate the results of the cluster analysis. 

B.2.2 Discriminant Analysis 

B.2.2.1 Description of the Method. Discriminant analysis uses one 
classification variable and several continuous quantitative variables to assign 
each object to a class corresponding to a value of the classification variable 
using the information contained in the continuous variables. In this study, 
hurricanes were the objects to be classified, the cluster identification number 
obtained from the cluster analysis was the classification variable, and 
hurricane parameters were the continuous variables. 

There are several types of discriminant analysis, some are based on the 
assumption that each class can be considered normally distributed while others 
use non-parametric methods and do not require the assumption of normality. In 
this study, we used the "k-neares t-neighbor" discriminant analysis, where k was 
chosen to be seven, equal to the number of parameters (P , R, 9, T, m, 4> and A) 
used in the analysis. 

Considering each hurricane as an object represented by a vector of seven 
components (P R, 9, T, m, <t> and A), the method computes the distance between 
two objects based on the total-sample covariance matrix (Mahalanobis distance), 
and, for each object, it saves the distances of the seven nearest objects 
(because k = 7). Based on these distances, it computes the probability that an 
object would fall into the class with the selected nucleus object. If the 
probability exceeds a specified threshold, the associated object is classified 
into that class. The actual computation was performed using the NEIGHBOR 
procedure of the SAS system. More details of the method are given in the SAS 
User's Guide (SAS 1982). 

B.2.2 .2 Rationale for Choice. The k-nearest-neighbor approach was non- 
parametric and did not require the assumption of normality. It allowed us to 
evaluate the results of the cluster analysis and to determine a number of 
clusters that could be characterized as homogeneous for testing the independence 
of the various hurricane parameters. 

B.2.2 .3 Limitations of the Method. The variables, except for the classification 
variable, must be continuous, so that the computation of distances can be 
performed. The classification variable can be either categorical or numerical, 
but there can only be one classification variable. It is recommended that the 
classification variable be limited to a finite number of values, so that the 
classes can be kept to a manageable number. 

187 



3.2.2.4 Interpretation of the Results. The discriminant analysis gives the 
classification of each object and probabilities of its membership in all the 
classes in which it could have been placed. By comparing the class that the 
object was placed in and the class assigned a priori, misclassif ied objects can 
be identified. The probability of membership in a particular class can be used 
to judge whether the classification of the object was appropriate. The threshold 
probability for the classification is user specified. In this study, the 
threshold probability was not assigned and objects were classified into the 
class which was associated with the largest membership probability. 

3.2.3 Principal Component Analysis 

3.2.3.1 Description of the Method. Given N numerical characteristics that 
describe a set of objects, the principal component analysis procedure computes N 
principal components; each principal component is a linear combination of the 
original characteristics (variables). The coefficients of this linear 
combination are the elements of an eigenvector of the correlation or covariance 
matrix of the original variables. The eigenvectors are normalized to have unit 
length (unit norm). The eigenvalues are the variances of the associated 
principal components. The first principal component has the largest eigenvalue 
and the N-th principal component has the smallest. The eigenvectors are 
orthonormal, i.e., they represent perpendicular directions in the space of 
original characteristic variables. In this study, the original characteristic 
variables were P , R, 9, T, m, <j) and \ therefore, there were seven principal 
components. 

The computation of the principal components of the hurricane parameters was 
performed using the PRINCOMP procedure of the SAS system. The procedure gives 
the percentage and cumulative percentage of all eigenvalues ordered from the 
largest to the smallest, i.e., from the first principal component to the seventh 
principal component. These percentages show the relative amount of variance 
accounted for by the principal components. The procedure also gives eigenvectors 
whose elements are interpreted as the loadings on the original variables; the 
loadings explain the relative importance of the hurricane parameters in each 
principal component. 

3.2.3.2 Rationale for Choice. After investigating the results of cluster 
analysis and discriminant analysis, we decided to examine the importance of 
various parameters in the grouping of hurricanes. The loadings provided with the 
principal component analysis allowed us to evaluate the weight of individual 
parameters. By plotting one principal component versus another and using the 
cluster identification number of each hurricane for the plotting symbol, we could 
examine the clustering patterns of the hurricanes. Using such a plot, we could 
deduce which parameter(s) had most control on the clustering. 

B.2.3.3 Limitations of the Method. Principal component analysis required that 
all seven parameters P , R, 0, T, m, (f> and A be available for each hurricane. 
Storms with missing values had to be excluded from the analysis. 

B.2.3.4 Interpretation of the Results. As explained above, the results of the 
principal component analysis can be used to explain the relative importance of 
the original variables for the grouping of hurricanes. By investigating the 
percentage of variance accounted for by each principal component, we were able to 

188 



select Che more important principal components. Then, by examining the 

eigenvectors associated with these principal components, we found the original 
variables that were most important in defining these principal components. 
Although the results of the principal component analysis can be used to explain 
some linear relations between the hurricane parameters, interpretation of these 
relations was not always clear. Sometimes scatter diagrams of the original 
variables were used for additional .guidance in understanding the results. 

B.2.4 Mann-Whitney Test 

B.2.4.1 Description of the Method. The Mann-Whitney test is a rank test 
(non-parametric). In this study, we divided the hurricanes into several a priori 
groupings based on location along the coast. For each test, we selected two 
groups of hurricanes: one group had N hurricanes and the other had M 

hurricanes. Assuming that each group was a random sample drawn from its 
respective population and two groups were mutually independent, we performed the 
Mann-Whi tney test on each of the hurricane parameters P , R and T. 



The test was performed in the following manner: We first combined the group of 
N hurricanes (group 1) with the group of M hurricanes (group 2). To test whether 
parameter P , for example, has the same distribution function in groups 1 and 2 , 
we first arranged the P Q in the mixed sample from the smallest to the largest 
value and assigned rank values from 1 to N+M to these P values. For tied values 
of P , an averaged rank value was assigned to each of them as shown in the 



following example (note rank 6.5 for P 



961.7) 



Example 



Rank 



Group Origin 



943.0 
947.2 
955.3 
956.7 
959.0 
961.7 
961.7 
966.5 
975.0 
979.0 
981.0 



1 


2 


2 


2 


3 


2 


4 


1 


5 


2 


6.5 


2 


6.5 


1 


8 


1 


9 


1 


10 


2 


11 


1 



Then, the sums of ranks (S) were computed separately for groups 1 and 2. In the 



38.5 and S = 27.5, 



The corresponding test statistics of the 



Mann-Whitney test were computed using the formulae: 



This example is for illustration only, not to be confused with any actual 
grouping in this study. 



189 



W x = S 1 - \ N (N + 1), » 2 -S' 2 - 2 -M(M+l) 

respectively for groups 1 and 2. In the example, N = 5 and M = 6, 
and W2 = 6.5. 

For given sample sizes N and M, percentiles of the Mann-Whitney test statistic 
can be computed (see Conover, 1971, table 8). We used a two-tailed test at 
5-percent significance level and the null hypothesis that P Q had the same 
distribution function in both groups of hurricanes. For N = 5 and M = 6 in the 
example, the 0.025-th percentile was 4 and the 0.975-th percentile was 26. 
Comparing the test statistics Wj and W 2 with these percentiles, we found that W, 
and W 2 were within the range between 4 and 2 6 (respectively, 0.025-th and 
0.975-th percentiles), and we accepted the null hypothesis for the above example. 

The test was repeated for R and T for every selected pair of groups of 
hurricanes in this study. For more details of the Mann-Whitney test, see 
Conover (1971). 

3.2.4.2 Rationale for Choice. The limited sample size and large natural 

variability of our hurricane data sample prevented us from reliably estimating 
the distribution functions of hurricane parameters for formal hypothesis 
testing. Since the Mann-Whitney test is a non-parametric test, it does not 
require a priori assumptions about the distribution function of the data sample 
and is suitable for our hurricane data. 

B.2.4.3 Limitations of the Method. The basic assumption for the Mann-Whitney 
test is that both groups are drawn as random samples. For the reasons discussed 
in Section 3.2.1.2, we did not consider it appropriate to use direction of 
landf ailing hurricanes as a random variable, and this parameter was excluded 
from the Mann-Whitney test. Another assumption of the Mann-Whitney test is that 
two samples must be mutually independent. There was no evidence that our 
hurricane data samples for the selected coastal segments violated this 
assumption. 

B.2.4.4 Interpretation of the Results. The Mann-Whitney test examines the 
similarity of two distributions of rankings, but not the distributions of the 
actual values of the hurricane parameters. For this reason, the results must be 
interpreted with caution, and any conclusions drawn from the test results must 
recognize that the distributions of rankings may not fully correspond to the 
distributions of the actual values. 

B.3 Methods for the Test of Independence 

To test independence among hurricane parameters, we used two methods: the 
Spearman test and contingency tables with the Chi-square test. The Spearman test 
is a rank test while the contingency tables with the Chi-square test is for 
categorical data. 



190 



B.3.1 Spearman Test 

B.3.1.1 Description of the Method. As an example, consider the Spearman test 
for P and R for a group of hurricanes. P Q was ranked from the smallest to the 
largest value and rank numbers were assigned to each value; for tied values of 
P , an average rank value was assigned to each of them as was done in the 
Mann-Whitney test (see sec. B.2.4.1). For the same group of hurricanes, R's were 
also ranked and assigned a rank number. Then the Spearman correlation was 
computed using the following formula: 



P = 1 - 



6W 



N 2 



N (IT-1) 



where W = V" [r(P Q ) - r(R.)] 2 



The parameter N is the sample size of the group of hurricanes, and r is the rank 
value of parameters P Q or R. Spearman's correlation can be used as a test 
statistic. Given the sample size, N, and the probability of a percentile, this 
percentile can be computed. 

There are three ways to test the Spearman correlation. The null hypothesis for 
all three tests is that P and R are mutually independent, that is, the 
correlation coefficient is not significantly different from zero. The alternate 
hypothesis for the first test is that P and R are positively correlated, for the 
second, that P and R are negatively correlated, and for the third, that P and R 
are correlated (either positively or negatively). In this study, when the 
probability associated with a specific estimate of P was greater than 
95th percentile, we rejected the null hypothesis of the first test, when p was 
less than 5th percentile, we rejected the null hypothesis of the second test, and 
when p was either less than 2.5 percent or greater than 97.5 percent, we rejected 
the null hypothesis of the third test. The significance level for all the tests 
was 5 percent. For more details, see Conover (1971). 

B.3.1. 2 Rationale for Choice. We chose Spearman test for the hurricane 
parameters because it offered the possibility of detecting the nature of 
interrelations, if they existed. 

B.3.1. 3 Limitations of the Method. As with many non-parametric tests, weak 
relations between two parameters may not be detected. 

B.3.1. 4 Interpretation of the Results. The Spearman test detects the 

correlation of ranks of random variables instead of the actual values of the 

variables. The interpretation of these correlations should be limited to the 

correlations of ranks only; independence between ranks of random variables may 
imply independence of the random variables. 



191 



B.3.2 Contingency Table with Chi-square Test 

B.3.2.1 Description of the Method. The contingency table with a Chi-square test 
was used at the 0.05 level and is described in detail in Section 4.2 of this 
report. Additional details may be found in Conover (1971). 

B.3.2 .2 Rationale for Choice. There was no requirement that the sample meet 
conditions other than it be a random sample of sufficient size. This made it 
suitable for use with our data sample. 

B.3.2 .3 Limitations of the Method. The contingency table with the Chi-square 
test was designed for categorical data samples, thus, we had to choose specific 
values to partition the parameters into categories to establish the cell 
frequencies in the contingency table. There cannot be more than 2 percent of 
cells which have expected frequency less than 5 in each of them. This limitation 
is to ensure that the Chi-square approximation is valid for the test. 

B.3.2 .4 Interpretation of the Results. The results of this test were sensitive 

to the values selected to partition the data into categories. A small change of 

the dividing value sometimes caused the result to change from not significant to 

significant, or vice versa. Therefore, we had to be careful in interpreting the 
results using this approach. 



APPENDIX C 

Plotting Position Formula 

C.l Introduction 

A plotting position formula was used to determine the location along the 
abscissa of ranked data in the cumulative frequency curves for the hurricane 
parameters. A plotting position formula was selected for this purpose from eight 
existing formulae based upon five evaluation criteria. 

Existing plotting position formulae are listed in Table C.l. The symbols used 
in the formulae are explained in the note underneath the table. In each line, 
the name of the formula is given in the left column, and the year in which the 
formula was introduced is given in the right column. This table does not include 
all existing formulae. The Beard (1943) formula is not included because it only 
applies to m = 1, and the Samsioe formula (see Reinius 1949, p. 51) is not 
included because its computation involves solving a N-th power equation and it is 
not easy to use. For convenience of computation, only easy-to-use formulae were 
considered. 

C.2 Criteria for Evaluation 

The plotting position formula listed in Table C.l were evaluated according to 
the criteria listed below. 

1. The plotting position must be such that all the observed data can 
be plotted on probability paper. 



192 



Table C.l. — List of plotting position formulae 



Name Formula ' Year 



California P„, = -£- 1923 

m N 

Hazen P„, = 2 ?~ 1 193 

m ZN 



Wei bull P m = t~ 193 9 

m N+l 

Chegodayev P„ = g~j 1955 



Blora P = *.',, 1958 



m 


N+0.4 




m-3/8 


m 


N+l/4 




3m-l 


m 


3N+1 




m-0.44 


m 


N+0.12 


> — 


m-0.3 7 



Tukey P = ";" t 1962 

J m 3N+1 

m -0 .44 
Gringorten P m = „, n ,_ 1963 



Reinius P = !" " '" 4 1982 

m N+0 .2 6 

P = probability; 

Til 

N = total number of items; 

m = rank of an item 

m < N. 



2. Tbe plotting position sbould lie between the observed frequencies 
(m-l)/N and m/N. (For the explanation of m and N, see the footnote 
of Table C.l.) 

3. The return period of a value equal to, or larger than, the largest 
observed value should converge towards N. 

4. The observed values should be equally spaced on the frequency 
scale. 

5. The plotting position should have an intuitive meaning, be 
analytically simple, and be easy to use. 



193 



Table C.2. — List of plotting position formulae in the descending order of their 
p * s. (See table C-l for the meanings of symbols.) 



m = 1 m = N 

California California 

Wei bull Haze n 

Chegodayev Gringorten 

Tukey Blora 

Reinius Reinius 

Bl om Tukey 

Gringorten Chegodayev 

Hazen Wei bull 



C.3 Evaluation of Plotting Position Formulae 

All formulae in Table C.l meet criteria 4 and 5. All except tbe California 
formula meet criteria 1 and 2. Only the California and Weibull formulae meet 
criterion 3. The most important problem with the California formula is that it 
gives p ffl = 100 percent for m = N, and this p can not be plotted on a probability 
paper. The most important advantage of Weibull formula is that tbe return period 
for m = 1 converges towards N as N * oo. Among formulae listed in Table C.l, 
only the Weibull formula meets all tbe criteria listed above. Thus, the Weibull 
formula was the choice used in this study. 

C.4 Comparison of Formulae 

To reveal more about the characteristics of the various formulae, we compared 
them for the special cases: m = 1, m = N, and N » oo. For m = 1 and N, the 
names of formulae are listed in Table C.2 in the descending order of their values 
of p . The order of names for m = N is exactly the reverse of that for m = 1, 
except for California formula. For N » oo, the values of p computed using all 
the formulae in Table C.l approach m/N. 

Since the sample size of hurricane clima tological data is usually small, we 

choose N = 10 for an example to compare values of p of the formulae in 

Table C.l. These values are plotted in Figure C.l. The Weibull formula gave the 

largest p for m = 1 and the smallest p for m = N. Except for the California 

formula, the largest difference in p between different formulae was less than 

5 percent. For m = 1, the p of the Weibull formula is approximately two times 

that of the Hazen formula. For m = N, the p of the Weibull formula is close to 

' r m 
that of the Hazen formula: approximately 91 percent compared to 95 percent. 



194 



3 

7 

6 

m s 

4 
3 
2 



CALIFORNIA 

HAZEN 

WEIBULL 

CHEGODAYEV 




1 0.1 0.2 0.5 I 2 5 10 



m 



90 95 99 99.6 99. 9< 



Figure C.l .--Comparison of plotting position formulae for N = 10. (See Cable C.l 
for the meanings of symbols.) 



95 



(Continued from inside front cover) 

NWS 16 Storm Tide Frequencies on the South Carolina Coast. Vance A. Myers, June 1975, 79 p. (C0M-75- 
11335) 

NWS 17 Estimation of Hurricane Storm Surge in Apalachicola Bay, Florida. James E. Overland, June 1975. 
66 p. (COM-75-11332) 

NWS 18 Joint Probability Method of Tide Frequency Analysis Applied to Apalachicola Bay and St. George 
Sound, Florida. Francis P. Ho and Vance A. Myers, November 1975, 43 p. (PB-251123) 

NWS 19 A Point Energy and Mass Balance Model of a Snow Cover. Eric A. Anderson, February 1976, 150 p. 
(PB-254653) 

NWS 20 Precipitable Water Over the United States, Volume 1: Monthly Means. George A. Lott, November 
1976, 173 p. (PB-264219) 

NWS 20 Precipitable Water Over the United States, Volume II: Semimonthly Maxima. Francis P. Ho and 
John T. Riedel, July 1979, 359 p. (PB-300870) 

NWS 21 Interduration Precipitation Relations for Storms - Southeast States. Ralph H. Frederick, March 
1979, 66 p. (PB-297192) 

NWS 22 The Nested Grid Model. Norman A. Phillips, April 1979, 89 p. (PB-299046) 

NWS 23 Meteorological Criteria for Standard Project Hurricane and Probable Maximum Hurricane and 
Probable Maximum Hurricane Windf ields , Gulf and East Coasts of the United States. Richard W. 
Schwerdt, Francis P. Ho, and Roger R. Watkins , September 1979, 348 p. (PB-80 117997) 

NWS 24 A Methodology for Point-to-Area Rainfall Frequency Ratios. Vance A. Myers and Raymond M. Zehr, 
February 1980, 180 p. (PB80 180102) 

NWS 25 Comparison of Generalized Estimates of Probable Maximum Precipitation With Greatest Observed 
Rainfalls. John T. Riedel and Louis C. Schreiner, March 1980, 75 p. (PB80 191463) 

NWS 26 Frequency and Motion of Atlantic Tropical Cyclones. Charles J. Neumann and Michael J. Pryslak, 
March 1981, 64 p. (PB81 247256) 

NWS 27 Interduration Precipitation Relations for Storms — Western United States. Ralph H. Frederick, 

John F. Miller, Francis P. Richards, and Richard W. Schwerdt, September 1981, 158 p. (PB82 230517) 

NWS 28 GEM: A Statistical Weather Forecasting Procedure. Robert G. Miller, November 1981, 103 p. 

NWS 29 Analyses of Elements of the Marine Environment for the Atlantic Remote Sensing Land Ocean 
Experiment (ARSLOE) — An Atlas for October 22 Through October 27, 1980. Lawrence D. Burroughs, 
May 1982, 116 p. (PB82 251281) 

NWS 30 The NMC Spectral Model. Joseph G. Sela, May 1982, 38 p. (PB83 115113) 

NWS 31 A Monthly Averaged Climatology of Sea Surface Temperature. Richard W. Reynolds, June 1982, 37 p. 
(PB83 115469) 

NWS 32 Pertinent Meteorological and Hurricane Tide Data for Hurricane Carla. Francis P. Ho and John F. 
Miller, August 1982, 111 p. (PB83 118240) 

NWS 33 Evaporation Atlas for the Contiguous 48 United States. Richard K. Farnsworth, Edwin S. Thompson, 
and Eugene L. Peck, June 1982, 26 p. 

NWS 34 Mean Monthly, Seasonal, and Annual Pan Evaporation for the United States. Richard K. Farnsworth 
and Edwin S. Thompson, December 1982, 85 p. (PB83 161729) 

NWS 35 Pertinent Meteorological Data for Hurricane Allen of 1980. Frances P. Ho and John F. Miller 
September 1983, 73 p. (PB 272 112) 

NWS 36 Water Available for Runoff for 1 to 15 Days Duration and Return Periods of 2 to 100 Years for 
Selected Agricultural Regions in the Northwest United States. Frank P. Richards, John F. Miller, 
Edward A. Zurndorfer, and Norma S. Foat, April 1983, 59 p. (PB84 120591) 

NWS 37 The National Weather Service Hurricane Probability Program. Robert C. Sheets, April 1984, 70 p. 
(PB84 182757) 



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serials; and miscellaneous technical publications. 

TECHNICAL REPORTS— Journal quality with 
extensive details, mathematical developments, or 
data listings. 

TECHNICAL MEMORANDUMS— Reports of 
preliminary, partial, or negative research or tech- 
nology results, interim instructions, and the like.